Number 2

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Title: Number 2

1
Number 2

Place value

2
Number 2 level descriptors

LEVEL 3 WRITE NUMBERS IN WORDS
LEVEL 4 MULTIPLY BY POWERS OF 10
ORDER WHOLE NUMBERS
MULTIPLY BY MULTIPLES OF 10
LEVEL 5 ROUND NUMBERS TO NEAREST 1, 10, etc
ROUND NUMBERS TO ONE AND TWO DECIMAL PLACES

LEVEL 6 ORDER DECIMAL NUMBERS
APPROXIMATE DECIMALS TO A SENSIBLE DEGREE OF
ACCURACY
LEVEL 7 ESTIMATE TO 1, 2 AND 3 SIGNIFICANT
FIGURES SF
USE SF TO ESTIMATE CALCULATIONS
LEVEL 8
SOLVE PROBLEMS USING STANDARD FORM

3
KEY WORDS

ESTIMATE
INTEGER
MULTIPLY
DIVIDE
APPROXIMATE
ROUNDING
MULTIPLES

PLACE VALUE
POWERS
ORDER
DECIMAL PLACE
SIGNIFICANT FIGURES
STANDARD FORM

4
NUMBERS IN WORDS

OBJECTIVE
LEVEL 3 UNDERSTAND HOW TO WRITE NUMBERS IN WORDS

SUCCESS CRITERIA
WRITE NUMBERS OF INCREASING MAGNITUDE IN WORDS
CONVERT NUMBERS WRITTEN IN WORDS INTO DECIMAL
NUMBERS

5
TYPES OF NUMBER

Counting numbers 1, 2, 3, 4, 5,
Natural numbers 1, 2, 3, 4, 5,
Odd numbers 1, 3, 5, 7, 9,
Even numbers 2, 4, 6, 8, 10,
Integers ,-2, -1, 0, 1, 2,
Positive integers 1, 2, 3, 4,
Negative integers -1, -2, -3, -4, -5,

6
Match the words to the numbers Match the words to the numbers Match the words to the numbers Match the words to the numbers Match the words to the numbers Match the words to the numbers

Sixty two thousand and five 60025 Sixty two thousand and five 60025
Sixty thousand two hundred and five 625 Sixty thousand two hundred and five 625
Six thousand two hundred and fifty 60205 Six thousand two hundred and fifty 60205
Sixty thousand and twenty five 6025 Sixty thousand and twenty five 6025
Sixty two thousand five hundred 600025 Sixty two thousand five hundred 600025
Six hundred and twenty five 62005 Six hundred and twenty five 62005
Six thousand and twenty five 6205 Six thousand and twenty five 6205
Six thousand two hundred and five 62500 Six thousand two hundred and five 62500
Six hundred thousand and twenty five 6250 Six hundred thousand and twenty five 6250
7
Complete the table
millions Hundred thousands Ten thousands thousands hundreds tens units words
3 4 0 9 0 thirty four thousand and ninety
three million and fifty six
4 0 0 0 0 9 3
three hundred and fifty six thousand
3 6 2 9 9 0
4 5 2 9
2 4 7 1 8
3 4 2 1 8 5
8
CREATE YOUR OWN whole numbers in words
NUMBER IN WORDS

9
What does the 9 represent in each case
9 653 Nine thousand or 9000
85 096
49 632
839
9 828 400
96 000 000
10
What does the 9 represent in each case
9 653 Nine thousand or 9000
85 096
49 632
839
9 828 400
96 000 000
Nine tens or 90
Nine thousands or 9000
Nine units or 9
Nine million or 9000 000
Ninety million or 90 000 000
11
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12
Write out the decimal numbers in words
5.96 Five point nine six
98.7
2.945
52.87
96.709
0.009
0.06
Note the most common mistake is to say 5.96 is
five point ninety six. This is five point nine
six
13
Write out the decimal numbers in words
5.96 Five point nine six
98.7
2.945
52.87
96.709
0.009
0.06
Ninety eight point seven
Two point nine four five
Fifty two point eight seven
Ninety six point seven zero nine
Zero point zero zero nine
Zero point zero six
Note the most common mistake is to say 5.96 is
five point ninety six. This is five point nine
six
14
CREATE YOUR OWN decimal numbers in words
NUMBER IN WORDS

15
What does the 4 represent in each case
53.47 Four tenths or 4/10
8.504 Four thousandths or 4/1000
9.642 Four hundredths or 4/100
83.49
6.84
93.004
16
What does the 4 represent in each case
53.47 Four tenths or 4/10
8.504 Four thousandths or 4/1000
9.642 Four hundredths or 4/100
83.49
6.84
93.004
Four tenths or 4/10
Four hundredths or 4/100
Four thousandths or 4/1000
17
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18
NUMBERS IN WORDS REVIEW

WRITE NUMBERS OF INCREASING MAGNITUDE IN WORDS
CONVERT NUMBERS WRITTEN IN WORDS INTO DECIMAL
NUMBERS
IDENTIFY MAGNITUDE BY POSITION

19
MULTIPLY AND DIVIDE BY POWERS OF 10

OBJECTIVE
LEVEL 4 UNDERSTAND HOW TO MULTIPLY AND DIVIDE BY
POWERS OF 10

SUCCESS CRITERIA
MULTIPLY BY 10 AND ADD A ZERO
MULTIPLY BY 100 AND ADD TWO ZEROS
MULTIPLY A DECIMAL BY 10 AND THE NUMBERS MOVE TO
THE LEFT
DIVIDE A DECIMAL BY 10 AND THE NUMBERS MOVE TO
THE RIGHT

20
Starter

1 1 1 1 1 1 1 1 1 1
5 5 5 5 5 5 5 5 5 5
8 8 8 8 8 8 8 8 8 8
Is there a quick way to add the same number ten
times?

21
Modulus

MODULUS means size irrespective of sign
-4 4 6 6 -0.06 0.06

22
The decimal point needs to be put back into the
number
7850 Seven point eight five
16300 Sixteen point three
47600 Four point seven six three
233000 Two hundred and thirty three
650000 Sixty five thousand
650000 Six thousand five hundred
650000 Six hundred and fifty
185730 Eighteen point five seven three
31200 Three hundred and twelve
07500 Zero point seven five
23
The decimal point needs to be put back into the
number
7 850 Seven point eight five
16 300 Sixteen point three
4 7630 Four point seven six three
233 000 Two hundred and thirty three
65000 0 Sixty five thousand
6500 00 Six thousand five hundred
650 000 Six hundred and fifty
18 5730 Eighteen point five seven three
312 00 Three hundred and twelve
0 7500 Zero point seven five
24
Multiply numbers by ten

When a number is multiplied by ten the modulus of
the number increases.
If a whole number is multiplied by 10 a zero is
placed on the right hand end of the number
16 10 160 7 10 70
If a decimal number is multiplied by 10 then the
numbers move one place to the left of the decimal
point and empty spaces are replaced by zeros
2.76 10 27.6 0.62 10 6.2

25
Multiply numbers by 10

Example 45 10 450
45 10
5 10
57 10
20 10
89 10
128 10
167 10
360 10

Example 5.7 10 57
5.1 10
9.2 10
12.8 10
10.9 10
6.056 10
0.67 10
0.061 10
0.0074 10

26
Multiply numbers by 10

Example 45 10 450
45 10 450
5 10 50
57 10 570
20 10 200
89 10 890
128 10 1280
167 10 1670
360 10 300

Example 5.7 10 57
5.1 10 51
9.2 10 92
12.8 10 128
10.9 10 109
6.056 10 60.56
0.67 10 6.7
0.061 10 0.61
0.0074 10 0.074

27
Multiply numbers by one hundred

When a number is multiplied by one hundred the
modulus of the number increases.
If a whole number is multiplied by 100 two zeros
are placed on the right hand end of the number
46 100 4600 8 100 800
If a decimal number is multiplied by 100 then the
numbers move two places to the left of the
decimal point and empty spaces are replaced by
zeros
2.6 100 260 0.38 100 38

28
Multiply numbers by 100

Example 37 100 3700
89 100
9 100
27 100
60 100
49 100
524 100
973 100
940 100

Example 5.7 100 570
8.1 100
3.2 100
16.8 100
14.9 100
8.056 100
0.95 100
0.039 100
0.0059 100

29
Multiply numbers by 100

Example 37 100 3700
89 100 8900
9 100 900
27 100 2700
60 100 6000
49 100 4900
524 100 52400
973 100 97300
940 100 94000

Example 5.7 100 570
8.1 100 810
3.2 100 320
16.8 100 1680
14.9 100 1490
8.056 100 805.6
0.95 100 95
0.039 100 3.9
0.0059 100 0.59

30
Divide numbers by 10

When a number is divided by ten the modulus of
the number decreases.
If a whole number is divided by 10 then the
numbers move one place to the right of the
decimal point and empty spaces are filled with
zeros
16 10 1.6 8 10 0.8
If a decimal number is divided by 10 then the
numbers move one place to the right of the
decimal point and empty spaces are filled with
zeros
14.6 10 1.46 0.46 10 0.046

31
Divide numbers by 10

Example 49 10 4.9
89 10
5 10
87 10
40 10
39 10
174 10
925 10
620 10

Example 9.5 10 0.95
65.1 10
43.2 10
6.8 10
4.9 10
7.046 10
0.51 10
0.064 10
0.0038 10

32
Divide numbers by 10

Example 49 10 4.9
89 10 8.9
5 10 0.5
87 10 8.7
40 10 4
39 10 3.9
174 10 17.4
925 10 92.5
620 10 62

Example 9.5 10 0.95
65.1 10 6.51
43.2 10 4.32
6.8 10 0.68
4.9 10 0.49
7.046 10 0.7046
0.51 10 0.051
0.064 10 0.0064
0.0038 10 0.00038

33
Divide numbers by 100

When a number is divided by one hundred the
modulus of the number decreases.
If a whole number is divided by 100 then the
numbers move two places to the right of the
decimal point and empty spaces are filled with
zeros
67 100 0.67 4 100 0.04
If a decimal number is divided by 100 then the
numbers move two places to the right of the
decimal point and empty spaces are filled with
zeros
67.8 100 0.678 0.86 100 0.0086

34
Divide numbers by 100

Example 49 100 0.49
89 100
63 100
7 100
90 100
73 100
714 100
953 100
630 100

Example 9.5 100 0.095
9.1 100
6.2 100
46.8 100
34.9 100
7.056 100
0.74 100
0.062 100
0.0094 100

35
Divide numbers by 100

Example 49 100 0.49
89 100 0.89
63 100 0.63
7 100 0.07
90 100 0.9
73 100 0.73
714 100 7.14
953 100 9.53
630 100 6.3

Example 9.5 100 0.095
9.1 100 0.091
6.2 100 0.062
46.8 100 0.468
34.9 100 0.349
7.056 100 0.07056
0.74 100 0.0074
0.062 100 0.00062
0.0094 100 0.000094

36
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38
Create and complete your own snake name
.
39
Multiply by Powers of 10 review

MULTIPLY BY 10 AND ADD A ZERO
MULTIPLY BY 100 AND ADD TWO ZEROS
MULTIPLY A DECIMAL BY 10 AND THE NUMBERS MOVE TO
THE LEFT OF THE DECIMAL POINT
DIVIDE A DECIMAL BY 10 AND THE NUMBERS MOVE TO
THE RIGHT OF THE DECIMAL POINT

40
ORDER WHOLE NUMBERS

OBJECTIVE
LEVEL 4 UNDERSTAND HOW TO ORDER WHOLE NUMBERS

SUCCESS CRITERIA
ORDER NEGATIVE NUMBERS
ORDER POSITIVE NUMBERS
ORDER INTEGERS

41
Complete the Number lines

-10 -10 -6 -6 0 0 2 2 4 4 8 8

-60 -60 -20 -20 0 0 40 40 80 80 100 100

-250 -250 -50 -50 0 0 250 250
42
Order whole numbers

We are often asked to place numbers in order of
size. We must remember that
Negative numbers are smaller than positive
numbers
Zero lies between the positive and negative
numbers
If in doubt think of a number line

43
Number lines

-10 -10 -8 -8 -6 -6 -4 -4 -2 -2 0 0 2 2 4 4 6 6 8 8 10 10

-100 -100 -80 -80 -60 -60 -40 -40 -20 -20 0 0 20 20 40 40 60 60 80 80 100 100

-250 -250 -200 -200 -150 -150 -100 -100 -50 -50 0 0 50 50 100 100 150 150 200 200 250 250
44
ORDER POSITIVE INTEGERS

Example
Place the following numbers in order, smallest
first
6, 8, 24, 17, 81, 12, 15
6, 8, 12, 15, 17, 24, 81

45
ORDER POSITIVE INTEGERS

Place the following sets of numbers in order,
smallest first.
12, 83, 27, 1, 5
30, 41, 5, 17, 46
41, 1, 24, 56, 28
12, 91, 72, 8, 93
81, 93, 56, 34, 9

Place the temperatures in order, highest to
lowest
760C, 210C, 260C
150C, 180C, 160C
910C, 120C, 390C
510C, 170C, 560C
190C, 160C, 730C

EXTENSION calculate the totals for each
question 1
46
ORDER POSITIVE INTEGERS

Place the following sets of numbers in order,
smallest first.
1, 5 , 12, 27, 83
5, 17, 30, 41, 46
1, 24, 28, 41, 56
8, 12, 72, 91, 93
9, 34, 56, 81, 93

Place the temperatures in order, highest to
lowest
210C, 260C, 760C
150C, 160C, 180C,
120C, 390C, 910C
170C, 510C, 560C
160C, 190C, 730C

EXTENSION 128, 123
47
ORDER NEGATIVE INTEGERS

Example
Place the following numbers in order, smallest
first
-6, -8, -4, -7, -18, -2, -5
-18, -8, -7, -6, -5, -4, -2

48
ORDER NEGATIVE INTEGERS

Place the following sets of numbers in order,
smallest first.
-2, -8, -17, -1, -52
-3, -4, -8, -27, -16
-3, -18, -2, -76, -26
-7, -9, -2, -18, -28
-8, -56, -42, -37 -92

Place the temperatures in order, highest to
lowest
-150C, -20C, -160C
-120C, -80C, -60C
-90C, -150C, -190C
-50C, -70C, -90C
-120C, -60C, -80C

EXTENSION calculate the totals for each
question 1
49
ORDER NEGATIVE INTEGERS

Place the following sets of numbers in order,
smallest first.
-52, -17, -8, -2, -1
-27, -16, -8, -4, -3
-76, -26, -18, -3, -2
-28, -18, -9, -7, -2
-92, -56, -42, -37 -8

Place the temperatures in order, highest to
lowest
-160C, -150C, -20C
-120C, -80C, -60C
-190C, -150C, -90C
-90C, -70C, -50C
-120C, -80C, -60C

EXTENSION -80, -33
50
ORDER INTEGERS

Example
Place the following numbers in order, smallest
first
6, 0, -8, 4, 7, 8, -2, -5
-8, -5, -2, 0, 4, 6, 7, 8

51
ORDER INTEGERS

Place the temperatures in order, lowest to
highest
60C, 20C, 80C, -50C, -20C, -60C
50C, 80C, 00C, -20C, -80C, -60C
10C, 120C, 90C, -90C, -150C, -190C
50C, 70C, 60C, 00C, -70C, -90C
190C, 160C, 70C, -120C, -60C, -80C
What is the difference between the highest and
lowest values

EXTENSION calculate the totals for each set of
values
52
ORDER INTEGERS

Place the temperatures in order, lowest to
highest
-60C, -50C, -20C, 20C, 60C, 80C
-80C, -60C, -20C, 00C, 50C, 80C
-190C, -150C, -90C, 10C, 90C, 120C
-90C, -70C, 00C, 50C, 60C, 70C,
-120C, -80C, -60C, 70C, 160C, 190C
14, 16, 31, 16, 31

EXTENSION 1, -3, -21, 2,16
53
ORDER INTEGERS

-60C, -40C, -20C, 00C, 20C, 40C, 60C , 80C
Calculate the total for the temperatures
Which is the coldest temperature
List the three coldest temperatures
List the three highest temperatures
Extension
What is the difference between the highest and
coldest temperatures

54
ORDER INTEGERS

-60C, -40C, -20C, 00C, 20C, 40C, 60C , 80C
Calculate the total for the temperatures 8
Which is the coldest temperature -6
List the three coldest temperatures -6, -4, -2
List the three highest temperatures 4, 6, 8
Extension
What is the difference between the highest and
coldest temperatures 14

55
ORDER INTEGERS
5
7
1
3
0

Create the largest number using all five cards
Create the smallest number using all five cards
Create the largest number using only the four
smallest cards
Create a number from four cards that can be
divided by 2
Extension
Create a four digit number that is divisible by 3

56
ORDER INTEGERS
5
7
1
3
0

Create the largest number using all five cards
75310
Create the smallest number using all five
cards10357
Create the largest number using only the four
smallest cards, 5310
Create a number from four cards that can be
divided by 2, ends in 0
Extension
Create a four digit number that is divisible by
3, digits add up to a multiple of 3

57
Change in temperature

Calculate the temperature if it drops by 100C
from 70C
Calculate the temperature if it drops by 150C
from -20C
Calculate the temperature if it rises by 120C
from 40C
Calculate the temperature if it rises by 150C
from -80C

58
ORDER WHOLE NUMBERS REVIEW

ORDER NEGATIVE NUMBERS
ORDER POSITIVE NUMBERS
ORDER INTEGERS

59
Rounding numbers

OBJECTIVE
LEVEL 5 UNDERSTAND HOW TO ROUND INTEGERS AND
DECIMAL NUMBERS TO ONE AND TWO DECIMAL PLACES

SUCCESS CRITERIA
ROUND INTEGERS TO THE NEAREST 10 AND 100
ROUND DECIMAL NUMBERS TO ONE DECIMAL PLACE
ROUND DECIMAL NUMBERS TO TWO DECIMAL PLACES

60
Which is closer

Is 390 closer to 400 or 300
Is 7647 closer to 7640 or 7650
Is 4849 closer to 4900 or 4800
Is 38 closer to 100 or 0

61
Rounding Numbers

Rules for rounding numbers
To round to the nearest 10 we look at the number
in the units column
To round to the nearest 100 we look at the number
in the tens column
If the number is less than 5 we round down
If the number is 5 or greater we round up
Example Round 5946 to the nearest
a) 10 b) 100 c) 1000
a) 5950 b) 5900 c) 6000
Note 27 to the nearest 100 is 0
974 to the nearest 100 is 1000

62
Complete the table
Nearest 10 Nearest 100 Extension Nearest 1000
6794
9485
6328
593
786
78
82
17
78325
63
Complete the table
Nearest 10 Nearest 100 Extension Nearest 1000
6794 6790 6800 7000
9485 9490 9500 9000
6328 6330 6300 6000
593 590 600 1000
786 790 800 1000
78 80 100 0
82 80 100 0
17 20 0 0
78325 78330 78300 78000
64
Rounding Decimal numbers

Rules for rounding decimal numbers
To round to one decimal place we look at the
number in the second decimal place
To round to two decimal places we look at the
number in the third decimal place
If the number is less than 5 we round down
If the number is 5 or greater we round up
Example Round 48.7852 to
a) 3 dp b) 2 dp c) 1 dp
a) 48.765 b) 48.79 c) 48.8
Note 3.96 rounded to 1 decimal place is 4.0
4.796 rounded to 2 decimal places is 4.80

65
Complete the table
1 dp 2 dp Extension 3 dp
5.7626
94.7549
6.8463
8.7638
16.482
47.839
38.978
42.73
18.48
66
Complete the table
1 dp 2 dp Extension 3 dp
5.7626 5.8 5.76 5.763
94.7549 94.8 94.75 94.755
6.8463 6.8 6.85 6.846
8.7638 8.8 8.76 8.764
16.482 16.5 16.48 16.482
47.839 47.8 47.84 47.839
38.978 39.0 38.98 38.978
42.73 42.7 42.73 42.730
18.48 18.5 18.48 18.480
67
Round the number in the centre in different ways
68
Write a number in the centre and round in
different ways
69
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70
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71
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72
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73
Extension

Is it possible to round a number to a given
number of decimal places by rounding in stages.
Example round 7.3241 to 1 dp
7.3241 7.324 7.32 7.3
change to 3 dp then 2dp then 1dp
Will this method work for any number

5.247
74
Rounding numbers review

ROUND INTEGERS TO THE NEAREST 10 AND 100
ROUND DECIMAL NUMBERS TO ONE DECIMAL PLACE
ROUND DECIMAL NUMBERS TO TWO DECIMAL PLACES

75
Order decimal numbers

OBJECTIVE
LEVEL 6 UNDERSTAND HOW TO ORDER DECIMAL NUMBERS

SUCCESS CRITERIA
LOOK AT PLACE VALUE TO ORDER DECIMAL NUMBERS
MULTIPLY BY 10, 100, 1000 WHEN ORDERING DECIMALS

76
STARTER ORDER INTEGERS

Place the temperatures in order, lowest to
highest
60C, 20C, 80C, -50C, -20C, -60C
50C, 80C, 00C, -20C, -80C, -60C
10C, 120C, 90C, -90C, -150C, -190C
50C, 70C, 60C, 00C, -70C, -90C
190C, 160C, 70C, -120C, -60C, -80C
What is the difference between the highest and
lowest values

EXTENSION calculate the totals for each set of
values
77
ORDER INTEGERS

Place the temperatures in order, lowest to
highest
-60C, -50C, -20C, 20C, 60C, 80C
-80C, -60C, -20C, 00C, 50C, 80C
-190C, -150C, -90C, 10C, 90C, 120C
-90C, -70C, 00C, 50C, 60C, 70C,
-120C, -80C, -60C, 70C, 160C, 190C
14, 16, 31, 16, 31

EXTENSION 1, -3, -21, 2,16
78
Multiply by 1000

Multiply each set of numbers by 1000
15.798, 22.782, 35.562, 18.386, 39.784
23.42, 49.02, 89.34, 12.73, 27.56
38.12, 39.94, 29.48, 16.89, 27.39
3.82, 9.03, 6.37, 1.93, 7.48, 2.83
2.3, 4.7, 8.3, 2.5, 0.5, 0.6, 0.2, 0.4

79
Multiply by 1000 answers

Multiply each set of numbers by 1000
15798, 22782, 35562, 18386, 39784
23420, 49020, 89340, 12730, 27560
38120, 39940, 29480, 16890, 27390
3820, 9030, 6370, 1930, 7480, 2830
2300, 4700, 8300, 2500, 500, 600, 200, 400

80
ORDER DECIMAL NUMBERS

Rules to order decimal numbers method 1
First look at the whole number part of the
decimal number and place in order of size
Then look at the first decimal place and place in
order based on this number
Then move to the next decimal place and place in
order based on this number

81
ORDER DECIMAL NUMBERS

Example method 1
Place the following numbers in order, largest to
smallest
1.607, 1.67, 0.6, 0.7, 1.7, 0.76, 0.607
Look at the whole number part and arrange by
whole number
1.607, 1.67, 1.7, 0.6, 0.7, 0.76, 0.607
Look at the first decimal place and arrange in
order
1.7, 1.607, 1.67, 0.7, 0.76, 0.6, 0.607
Look at the next decimal place and arrange in
order
1.7, 1.67, 1.607, 0.76, 0.7, 0.6, 0.607
Look at the next decimal place and arrange in
order
1.7, 1.67, 1.607, 0.76, 0.7, 0.607, 0.6

82
ORDER DECIMALS
0.85
0.08
0.805
0.58
2.5
2.508

Which is the largest number
Which is the smallest number
Place the numbers in order of size, smallest
first
Extension
What is the difference between the smallest and
largest

83
ORDER DECIMALS
0.85
0.08
0.805
0.58
2.5
2.508

Which is the largest number 2.508
Which is the smallest number 0.08
Place the numbers in order of size, smallest
first
0.08, 0.58, 0.805, 0.85, 2.508
Extension
What is the difference between the smallest and
largest 2.5

84
ORDER DECIMAL NUMBERS

Place the following sets of numbers in order,
smallest first.
0.8, 0.4, 0.6, 0.5, 0.3
0.7, 0.77, 0.76, 0.07
0.45, 0.05, 0.4, 0.04
0.9, 0.2, 0.18, 0.28
0.56, 0.42, 0.37, 0.92
1.7, 1.8, 1.07, 1.08
3.5, 0.05, 2.05, 2.5

Place the following sets of numbers in order,
smallest first.
0.507, 0.57, 0.705, 0.75
0.604, 0.46, 0.406, 0.405
0.704, 0.074, 0.477, 0.774
1.507, 1.705, 1.075, 2.1
3.701, 2.509, 1.909, 4,39
2.009, 0.009, 0.034, 1.001
1.607, 1.76, 1.067, 1.007

EXTENSION calculate the totals for each
question 1
85
ORDER DECIMAL NUMBERS

Place the following sets of numbers in order,
smallest first.
0.3, 0.4, 0.5, 0.6, 0.8
0.07, 0.7, 0.76, 0.77
0.04, 0.05, 0.4, 0.45
0.18, 0.2, 0.28, 0.9
0.37, 0.42, 0.56, 0.92
1.07, 1.08, 1.7, 1.8
0.05, 2.05, 2.5, 3.5

Place the following sets of numbers in order,
smallest first.
0.507, 0.57, 0.705, 0.75
0.405, 0.406, 0.46, 0.604
0.074, 0.477, 0.704, 0.774
1.075, 1.507, 1.705, 2.1
1.909, 2.509, 3.701, 4,39
0.009, 0.034, 1.001, 2.009
1.007, 1.067, 1.607, 1.76

EXTENSION calculate the totals for each
question 1
86
ORDER DECIMAL NUMBERS

Rules to order decimal numbers method 2
Look at the numbers to be ordered, identify the
highest number of decimal places from the set of
numbers
If the highest number of decimal places is one
then multiply all numbers by 10
If the highest number of decimal places is two
then multiply all numbers by 100
If the highest number of decimal places is three
then multiply all numbers by 1000
This method converts all the decimal numbers into
whole numbers first, we then order the numbers.
We must remember to convert back at the end.

87
ORDER DECIMAL NUMBERS

Example method 2
Place the following numbers in order, largest to
smallest
1.607, 1.67, 0.6, 0.7, 1.7, 0.76, 0.607
Look at the number of decimal places, the biggest
number of decimal places is three
We must multiply every number by 1000 to give
1607, 1670, 600, 700, 1700, 760, 607
We now place this set of numbers in order
1700, 1670, 1607, 760, 700, 607, 600
We now divide all numbers by 1000 to give
1.7, 1.67, 1.607, 0.76, 0.7, 0.607, 0.6

88
ORDER DECIMALS
0.907
0.96
0.9
0.609
1.69
1.6

Multiply all numbers by 1000
Place the multiplied numbers in order, smallest
first
Place the original numbers in order, smallest
first
Extension
Add the numbers together

6.666
89
ORDER DECIMALS
0.907
0.96
0.9
0.609
1.69
1.6

Multiply all numbers by 1000
907, 1600, 1690, 609, 900, 960
Place the multiplied numbers in order, smallest
first
609, 900, 907, 960, 1600, 1690
Place the original numbers in order, smallest
first
0.609, 0.9, 0.907, 0.96, 1.6, 1.69
Extension
Add the numbers together 6.666

90
ORDER DECIMAL NUMBERS

Multiply each number by 100. Place the following
sets of numbers in order, smallest first.
0.8, 0.84, 0.86, 0.08
0.7, 0.77, 0.76, 0.07
0.45, 0.05, 0.4, 0.04
0.9, 0.2, 0.18, 0.28
0.56, 0.42, 0.37, 0.92
1.7, 1.8, 1.07, 1.08
3.5, 0.05, 2.05, 2.5

Multiply each number by 1000. Place the
following sets of numbers in order, smallest
first.
0.507, 0.57, 0.705, 0.75
0.604, 0.46, 0.406, 0.405
0.704, 0.074, 0.477, 0.774
1.507, 1.705, 1.075, 2.1
3.701, 2.509, 1.909, 4,39
2.009, 0.009, 0.034, 1.001
1.607, 1.76, 1.067, 1.007

EXTENSION calculate the totals for each
question 1
91
ORDER DECIMAL NUMBERS

Multiply each number by 100. Place the following
sets of numbers in order, smallest first.
0.8, 0.84, 0.86, 0.08
0.7, 0.77, 0.76, 0.07
0.45, 0.05, 0.4, 0.04
0.9, 0.2, 0.18, 0.28
0.56, 0.42, 0.37, 0.92
1.7, 1.8, 1.07, 1.08
3.5, 0.05, 2.05, 2.5

Multiply each number by 1000. Place the
following sets of numbers in order, smallest
first.
0.507, 0.57, 0.705, 0.75
0.604, 0.46, 0.406, 0.405
0.704, 0.074, 0.477, 0.774
1.507, 1.705, 1.075, 2.1
3.701, 2.509, 1.909, 4,39
2.009, 0.009, 0.034, 1.001
1.607, 1.76, 1.067, 1.007

EXTENSION calculate the totals for each
question 1
92
Place numbers in the empty boxes so they increase
in size NAME
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94
Order decimal numbers review

MULTIPLY BY 10, 100, 1000 TO ORDER DECIMALS
USE PLACE VALUE TO ORDER DECIMALS
ORDER DECIMALS WITH ONE DECIMAL PLACE
ORDER DECIMALS WITH TWO DECIMAL PLACES
ORDER DECIMALS WITH THREE DECIMAL PLACES

95
SENSIBLE DEGREE OF ACCURACY

OBJECTIVE
LEVEL 6 UNDERSTAND HOW TO APPROXIMATE DECIMALS
TO A SENSIBLE DEGREE OF ACCURACY

SUCCESS CRITERIA
DETERMINE THE SENSIBLE DEGREE OF ACCURACY
GIVE ANSWERS TO A SENSIBLE DEGREE OF ACCURACY

96
Starter how many decimal places are in each
number

4.78
5.059
0.05
0.0008

97
DETERMINE THE DEGREE OF ACCURACY

We are sometimes asked to give answers to a
sensible degree of accuracy.
To determine the degree of accuracy we must look
at the accuracy of the values given in the
question
If values are given to 3 decimal places then the
answer should be given to two decimal places
If the values given in the question are currency
then the answer should be given to 2 decimal
places to indicate pounds and pence

98
Determine the degree of accuracy

Example 1
A room is measured for carpet fitting. The
length of the room is 4.3 m and the width is 3.62
m
Calculate the area of the carpet required to a
sensible degree of accuracy

Answer
Area length width
Area 4.3 3.62
Area 15.566 m2
As the length and width were given to an accuracy
of up to 2 decimal places the area should be
given to the same degree of accuracy
Area 15.57 m2

99
Determine the degree of accuracy

Example 2
A 4.6 m length of timber is required to build a
fence. The timber costs 4.68 per metre
Calculate the cost of the length of timber

Answer
Cost length price per m
Cost 4.6 4.68
Cost 21.528
As the final answer is pounds and pence then a
sensible degree of accuracy would be 2 decimal
places.
Cost 21.53

100
Complete the table
Calculation Level of accuracy Answer
4.6 7.25 2 dp
2.8 3.50
3.52 2.43
7.642 7.2
14.6 37.2
4.63 1.24
5.216 0.63
101
Complete the table
Calculation Level of accuracy Answer
4.6 7.25 2 dp 33.35
2.8 3.50 2 dp 9.80
3.52 2.43 2 dp 8.55
7.642 7.2 3 dp 55.022
14.6 37.2 1 dp 543.12
4.63 1.24 2 dp 5.74
5.216 0.63 3 dp Ans. 2dp 3.29
102
SENSIBLE DEGREE OF ACCURACY REVIEW

DETERMINE THE SENSIBLE DEGREE OF ACCURACY
GIVE ANSWERS TO A SENSIBLE DEGREE OF ACCURACY

103
SIGNIFICANT FIGURES

OBJECTIVE
LEVEL 7 UNDERSTAND HOW TO APPROXIMATE NUMBERS
USING SIGNIFICANT FIGURES

SUCCESS CRITERIA
EXPRESS NUMBERS USING SIGNIFICANT FIGURES
APPROXIMATE CALCULATIONS USING SIGNIFICANT FIGURES

104
Starter

Why would the number one hundred and seventy
three be written like this?
173

105
Significant figures

The numbers 127, 6.24, 0.0278, 809, 0.504 and
62500 all have three significant figures
0.0278 has three significant figures as the
zeros at the front dont count
62500 has three significant figures as the zeros
at the end dont count
809 has three significant figures as the zeros
between other digits count

106
Significant figures

How many significant figures do these numbers
have?
2
91
183
408
87000
2408

How many significant figures do these numbers
have?
3.1
5.09
0.7
0.083
0.508
0.0006

107
Significant figures

How many significant figures do these numbers
have?
2 1 sf
91 2 sf
183 3 sf
408 3 sf
87000 2 sf
2408 4 sf

How many significant figures do these numbers
have?
3.1 2 sf
5.09 3 sf
0.7 1 sf
0.083 2 sf
0.508 3 sf
0.0006 1 sf

108
Rounding numbers using significant figures

Numbers can be rounded using significant figures
in much the same way as we round decimals.
If the digit in the next column of significance
is 5 or greater then we round up, else it stays
the same
347 rounded to 2 significant figures is 350

109
Estimate the following to one significant figure

17.5
128.9
0.67
0.37
0.92
0.029
0.079
0.052
0.0068

110
Estimate the following to one significant figure

20
100
0.7
0.4
0.9
0.03
0.08
0.05
0.007

111
Estimate the following to two significant figure

562
672
272
146
138
128
1560
37600
45200

45.9
386.9
0.268
0.382
0.578
0.0946
0.0942
0.00638
0.000836

112
Estimate the following to two significant figure

560
670
270
150
140
130
1600
38000
45000

46
39
0.27
0.38
0.58
0.095
0.094
0.0064
0.00084

113
Rounding numbers using significant figures
number 1 sf 2 sf 3 sf
346
2894
2.476
19.382
14.975
0.2784
0.003864
0.07399
0.799
114
Rounding numbers using significant figures
number 1 sf 2 sf 3 sf
346 300 350 346
2894 3000 2900 2890
2.476 2 2.5 2.48
19.382 20 19 19.4
14.975 10 15 15.0
0.2784 0.3 0.28 0.278
0.003864 0.004 0.0039 0.00386
0.07399 0.07 0.074 0.0740
0.799 0.8 0.80 0.799
115
Estimating using significant figures

Estimating is when we change numbers into numbers
we can use to calculate answers in our heads.
Round all numbers to 1 significant figure
37 9 40 10 400
We can now see that 37 9 should give a value
near 400

116
Estimate the answer example
117
Estimate answers to the following problems
118
answers

1
10 b) 0.6 c) 5
d) 5 e) 28 f) 450
2
9.66 b) 0.54 c) 5.2
d) 4.9 e) 26.9 f) 447

119
Create your own problem showing how you would
calculate an estimate of the answer.calculate
the actual answer. Then compare answers and
comment
120
SIGNIFICANT FIGURES REVIEW

EXPRESS NUMBERS USING SIGNIFICANT FIGURES
APPROXIMATE CALCULATIONS USING SIGNIFICANT FIGURES

121
STANDARD FORM

OBJECTIVE
LEVEL 8 UNDERSTAND HOW TO USE STANDARD FORM

SUCCESS CRITERIA
KNOW WHY WE USE STANDARD FORM
CONVERT NUMBERS INTO STANDARD FORM
CONVERT NUMBERS FROM STANDARD FORM
WHEN TO ADD AND SUBTRACT INDEX NUMBERS
USE STANDARD FORM IN CALCULATIONS (NON CALC)
USE STANDARD FORM IN CALCULATIONS (CALCULATOR)

122
STARTER COMPLETE THE TABLE
NUMBER TEN TIMES TEN DIVIDE POWER OF 10 WRITTEN 10n
10
100 1 10 10 102
1000 1 10 10 10
10000
100000
0.1
0.01 1 10 10 10-2
0.001 1 10 10 10
0.0001
0.00001
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Laws of indices

ya yb ya b
ya yb ya - b
(ya )b yab
y0 1 y1 y

125
Laws of indices ya yb ya b

Example
72 74 72 4 76
Exercise Simplify
32 34
54 55
88 84
61 65
92 96

126
Laws of indices ya yb ya - b

Example
76 74 76 - 4 72
Exercise Simplify
36 34
59 55
88 84
68 65
94 96

127
Laws of indices (ya)b ya byab

Example
(76)4 76 4 724
Exercise Simplify
(36)4
(59)5
(83)4
(68)5
(94)6

128
Laws of indices cont
129
Laws of indices cont
130
KNOW WHY WE USE STANDARD FORM

Standard form is used to express very large and
very small numbers in a different way
620000000000000 is a very large number
In standard form 620000000000000 6.2 1014
0.000000000017 is a very small number
In standard form 0.000000000017 1.7 10-12

131
CONVERT NUMBERS INTO STANDARD FORM

To write numbers in standard form they must
conform to these rules
A 10n
1 A lt10 and n is an integer
This means A must be greater than or equal to 1
but less than 10. It must have a single digit
(1, 2, 3, 4, 5, 6, 7, 8, 9) before the decimal
point.
n is a positive or negative whole number

132
CONVERT NUMBERS INTO STANDARD FORM

Example 1
Convert 267000 into standard form
The decimal point must move 5 places to give 2.67
267000 2.67 105

Example 2
Convert 34000 into standard form
The decimal point must move 4 places left to give
3.4
34000 3.4 104

133
CONVERT NUMBERS INTO STANDARD FORM

A 10n
290 2.9 102
7300 7.3 103
68000 6.8 104
72000 7.2 104
45100 4.51 103
742000 7.42 105

134
CONVERT NUMBERS INTO STANDARD FORM

1 Convert into standard form
120 1.2 102
450
270
780
6300
3400
2300
7800

2 Convert into standard form
620 6.2 102
950
1700
9830
2390
54000
83900
18000

135
CONVERT NUMBERS INTO STANDARD FORM

1 Convert into standard form
1900 1.9 103
2600
7900
8300
16000
39000
43000
28000

2 Convert into standard form
6500 6.5 103
9300
13000
94000
390000
240000
98000000
59000000

136
CONVERT NUMBERS INTO STANDARD FORM

Example 1
Convert 0.00056 into standard form
The decimal point must move 4 places to give 5.6
0.00056 5.6 10-4

Example 2
Convert 0.0058 into standard form
The decimal point must move 3 places to give 5.8
0.0058 5.8 10-3

137
CONVERT NUMBERS INTO STANDARD FORM

A 10n
0.037 3.7 10-2
0.0028 2.8 10-3
0.00038 3.8 10-4
0.00029 2.9 10-4
0.00582 5.82 10-3
0.0000283 2.83 10-5

138
CONVERT NUMBERS INTO STANDARD FORM

Convert into standard form
0.038 3.8 10-2
0.049
0.068
0.039
0.0032
0.0084
0.0067
0.00074

Convert into standard form
0.098 9.8 10-2
0.063
0.0048
0.0019
0.000062
0.000084
0.000000062
0.00000000293

139
CONVERT NUMBERS INTO STANDARD FORM

Convert into standard form
0.0028 2.8 10-3
0.0049
0.00068
0.00039
0.00032
0.000084
0.000067
0.0000074

Convert into standard form
0.0063 63 10-3
0.0042
0.00093
0.00049
0.000056
0.00000748
0.000000000412
0.0000000000843

140
CONVERT NUMBERS FROM STANDARD FORM

Example 1
Convert 5.39 104 into an ordinary number
The decimal point must move 4 places to the right
5.39 104 53900

Example
Convert 6.73 105 into an ordinary number
The decimal point must move 5 places to the right
6.73 105 673000

141
CONVERT NUMBERS FROM STANDARD FORM

Convert into ordinary numbers
5.3 102 530
3.8 102
3.5 102
2.4 102
3.5 103
9.3 103
5.27 103
5.034 103

Convert into ordinary numbers
6.5 103 6500
8.1 103
3.9 103
6.2 104
7.4 104
8.5 104
7.23 105
2.307 105

142
CONVERT NUMBERS FROM STANDARD FORM

Example 1
Convert 6.7 10-3 into an ordinary number
The decimal point must move 3 places to the left
6.7 10-3 0.0067

Example 2
Convert 8.31 10-3 into an ordinary number
The decimal point must move 3 places to the left
8.31 10-3 0.00831

143
CONVERT NUMBERS FROM STANDARD FORM

Convert into ordinary numbers
5.9 10-2 0.059
7.9 10-2
3.6 10-2
4.7 10-2
2.6 10-3
4.9 10-3
3.1 10-3
8.63 10-3

Convert into ordinary numbers
8.3 10-3 0.0083
2.9 10-3
1.8 10-3
9.5 10-3
8.4 10-4
9.8 10-4
2.8 10-4
4.35 10-4

144
WHEN TO ADD AND SUBTRACT INDEX NUMBERS

The number 107 is written in index form. The
number 10 is the base number and the number 7 is
the index number
107

Index number
Base number
145
WHEN TO ADD INDEX NUMBERS

When two index form numbers are multiplied
together and they have the same base we can add
the index numbers
103 105 103 5 108

146
WHEN TO ADD INDEX NUMBERS

Example 1
Simplify
104 103
The base numbers are the same so we can add the
index numbers
104 103 104 3 107

Example 2
Simplify
10-2 107
The base numbers are the same so we can add the
index numbers
10-2 107 10-2 7 105

147
WHEN TO ADD INDEX NUMBERS

Simplify
104 105 109
102 105
106 103
107 104
104 107
106 104
104 102
103 105

Simplify
104 107 1011
103 105
106 105
108 104
10-4 107
10-6 1014
10-4 107
10-3 105

148
WHEN TO ADD INDEX NUMBERS

Simplify
10-4 107 103
10-2 105
106 10-2
107 10-3
10-4 107
106 10-2
104 10-2
10-3 105

Simplify
10-2 10-7 10-9
10-3 10-5
10-4 10-5
10-8 10-3
10-4 10-8
10-6 10-4
10-4 10-6
10-3 10-8

149
WHEN TO SUBTRACT INDEX NUMBERS

When two index form numbers are divided and they
have the same base we can subtract the index
numbers
107 105 107 5 102

150
WHEN TO SUBTRACT INDEX NUMBERS

Example 1
Simplify
108 103
The base numbers are the same so we can add the
index numbers
108 103 108 3 105

Example 2
Simplify
10-5 103
The base numbers are the same so we can add the
index numbers
10-5 103 10-5 3 10-8

151
WHEN TO SUBTRACT INDEX NUMBERS

Simplify 1
109 107 102
108 105
107 103
105 104
108 103
105 103
104 102
102 105

Simplify 2
109 104 105
108 103
1011 103
107 104
10-5 10-2
10-2 103
104 10-2
10-8 10-3

152
WHEN TO SUBTRACT INDEX NUMBERS

Simplify 3
10-5 106 10-11
10-8 105
10-7 103
10-5 104
108 10-3
105 10-4
104 10-2
10-2 10-5

Simplify 4
10-7 10-5 10-2
10-6 10-2
10-1 10-3
10-7 10-3
10-8 10-4
10-2 10-8
10-9 10-2
10-8 10-5

153
USE STANDARD FORM IN CALCULATIONS (NON CALC)

We can simplify expressions given in standard
form using the skills we have gained.
Example
Simplify 3.0 105 4.0 103
Rearrange 3.0 4.0 105 103
Multiply together
Answer 12 108 1.2 109

154
USE STANDARD FORM IN CALCULATIONS (NON CALC)

Simplify 1
2.0 105 4.0 103
3.0 106 2.0 102
5.0 102 3.0 103
4.0 103 3.0 104
2.0 107 2.5 103
1.5 104 4.0 105
2.0 105 1.5 106
2.5 104 3.0 103

Simplify 2
2.0 106 2.5 104
1.5 105 4.0 106
2.0 106 1.5 107
2.5 105 3.0 108
2.0 104 4.3 102
3.4 103 2.0 104
5.0 104 2.1 105
4.0 103 3.1 104

155
USE STANDARD FORM IN CALCULATIONS (NON CALC)

We can simplify expressions given in standard
form using the skills we have gained.
Example
Simplify 8.0 105 (4.0 103)
Rearrange 8.0 4.0 105 103
Divide
Answer 2.0 102

156
USE STANDARD FORM IN CALCULATIONS (NON CALC)

Simplify 1
8.0 105 (4.0 103)
8.0 107 (2.0 102)
6.0 103 (3.0 107)
4.0 105 (2.0 106)
9.0 109 (3.0 102)
2.0 105 (4.0 103)
5.0 104 (2.5 104)
3.0 103 (1.5 106)

Simplify 2
6.0 105 (3.0 106)
9.0 107 (3.0 107)
6.0 103 (2.0 105)
4.0 105 (2.0 109)
5.0 109 (2.5 105)
2.0 105 (4.0 107)
9.0 104 (4.5 108)
7.0 103 (3.5 104)

157
USE STANDARD FORM IN CALCULATIONS (CALCULATOR)

To enter 105 into a calculator we must use the
raise to power button
8.6 105 when entered into a calculator we press
the buttons in this sequence
8.6 10 5 860000

xy
x
xy
158
USE STANDARD FORM IN CALCULATIONS (CALCULATOR)

Example
Simplify 3.2 108 4.0 1012
3.2 10 8 4.0 10 12 25.6 1020
3.2 108 4.0 1012 2.56 1021

xy
xy
159
USE STANDARD FORM IN CALCULATIONS (CALCULATOR)

Simplify 1
2.0 105 4.0 103
3.0 106 2.0 102
5.0 102 3.0 103
4.0 103 3.0 104
2.0 107 2.5 103
1.5 104 4.0 105
2.0 105 1.5 106
2.5 104 3.0 103

Simplify 2
2.0 106 2.5 104
1.5 105 4.0 106
2.0 106 1.5 107
2.5 105 3.0 108
2.0 104 4.3 102
3.4 103 2.0 104
5.0 104 2.1 105
4.0 103 3.1 104

160
USE STANDARD FORM IN CALCULATIONS (CALCULATOR)

Example
simplify 4.8 108
2.4 1012
4.8 10 8 (2.4 10 12) 2.0
10-4
4.8 108 2.0 10-4
2.4 1012

xy
xy
R
161
USE STANDARD FORM IN CALCULATIONS (NON CALC)

Simplify 1
8.0 105 (4.0 103)
8.0 107 (2.0 102)
6.0 103 (3.0 107)
4.0 105 (2.0 106)
9.0 109 (3.0 102)
2.0 105 (4.0 103)
5.0 104 (2.5 104)
3.0 103 (1.5 106)

Simplify 2
6.0 105 (3.0 106)
9.0 107 (3.0 107)
6.0 103 (2.0 105)
4.0 105 (2.0 109)
5.0 109 (2.5 105)
2.0 105 (4.0 107)
9.0 104 (4.5 108)
7.0 103 (3.5 104)

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STANDARD FORM REVIEW

KNOW WHY WE USE STANDARD FORM
CONVERT NUMBERS INTO STANDARD FORM
CONVERT NUMBERS FROM STANDARD FORM
WHEN TO ADD AND DIVIDE INDEX NUMBERS
USE STANDARD FORM IN CALCULATIONS (NON CALC)
USE STANDARD FORM IN CALCULATIONS (CALCULATOR)

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Number 2 level descriptors

OBJECTIVE
LEVEL 7 UNDERSTAND HOW TO ESTIMATE TO 1, 2 AND 3
SIGNIFICANT FIGURE

SUCCESS CRITERIA
KNOW WHY WE ESTIMATE NUMBERS
WRITE NUMBERS TO 1, 2 AND 3 SIGNIFICANT FIGURES
KEEP ZEROS TO MAINTAIN MAGNITUDE

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Number 2 level descriptors

OBJECTIVE
LEVEL 7 UNDERSTAND HOW TO ESTIMATE TO
SIGNIFICANT FIGURES TO FIND APPROXIMATE ANSWERS
TO PROBLEMS

SUCCESS CRITERIA
FIND APPROXIMATE SOLUTIONS TO PROBLEMS BY
ESTIMATING NUMBERS

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Number 2 level descriptors

OBJECTIVE
LEVEL 8 UNDERSTAND HOW TO WRITE NUMBERS IN
STANDARD FORM

SUCCESS CRITERIA
CONVERT A NUMBER WRITTEN IN DECIMAL FORM INTO
STANDARD FORM

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Number 2 level descriptors

OBJECTIVE
LEVEL 8 UNDERSTAND HOW TO WRITE STANDARD FORM
NUMBERS IN DECIMAL FORM

SUCCESS CRITERIA
CONVERT A NUMBER WRITTEN IN STANDARD INTO DECIMAL
FORM

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Number 2 level descriptors

OBJECTIVE
LEVEL 8 UNDERSTAND HOW TO SOLVE PROBLEMS USING
STANDARD FORM WITH A CALCULATOR

SUCCESS CRITERIA
USE THE XY BUTTON ON A CALCULATOR
USE BRACKETS TO KEY IN PROBLEMS

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Number 2 level descriptors

OBJECTIVE
LEVEL 8 UNDERSTAND HOW TO SOLVE PROBLEMS USING
STANDARD FORM

SUCCESS CRITERIA
USE THE LAWS OF INDICES TO MULTIPLY AND DIVIDE
NUMBERS WRITTEN IN STANDARD FORM
ADD AND SUBTRACT NUMBERS WRITTEN IN STANDARD FORM

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NUMBER STARTERS
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Write numbers in words