Whole Numbers How To Dissect And Solve Word Problems

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Chapter 3

• Decimals

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Decimals
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Learning Unit Objectives
Rounding Decimals Fraction and Decimal
Conversions
LU3.1

• Explain the place values of whole numbers and
  decimals round decimals
• Convert decimal fractions to decimals, proper
  fractions to decimals, mixed numbers to decimals,
  and pure and mixed decimals to decimal fractions

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Decimals
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Learning Unit Objectives
Adding, Subtracting, Multiplying, and Dividing
Decimals
LU3.2

• Add, subtract, multiply, and divide decimals
• Multiply and divide decimals by shortcut methods
• Complete decimal applications in foreign currency

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Decimal place-value chart

• Figure 3.1

Whole Number Groups
Decimal Place Values
Ten Thousandths
Hundredths
Thousandths
Hundred Thousandths
Decimal Point
Hundreds
Thousands
Tens
Ones
Tenths
1 10
1 . 100
1 . 1,000
1 . 10,000
1 . 100,000
1,000
100
10
1
and
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Rounding Decimals
Step 1. Identify the place value of the digit
you want to round
Step 3. Drop all digits to the right of the
identified digit

• .3272727

• .337272

Step 2. Identify the digit to the right. If 5 or
more, increase the identified digit by 1. If
less than 5 do not change
.33
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Rounding Decimals
.06 ---------------------gtThe 6 is in the
hundredths place value 1.527 --------------------
gt The 5 is in the tenths place value 2.8394
------------------gt The 4 is in the ten
thousandths place value
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Converting Decimal Fractions to Decimals
2 Steps 1. Count the number of zeros in the
denominator. 2. Place the numerator of the
decimal fraction to the right of the decimal
point the same number of places as you have zeros
in the denominator. Do not go over the total
number of denominator zeros.
Fraction Decimal of places
3 .3 1 10 3 .03 2 100 3
.003 3 1,000 3 .0003 4 10,000
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Converting Proper Fractions to Decimals
.75

• 4 3.00
• 2.8
• 20
• 20
• 0

EQUALS

• 3
• 4

.75
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Converting Mixed Numbers to Decimals
.4

• 5 2.0
• 2.0
• 0

(Step 1)

• 2
• 5

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8 .4 (Step 2)
8.4
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Converting Pure Decimals to Decimal Fractions
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Step 1
24 1
Step 2
.24
2
Places
24 100
Step 3
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Converting Mixed Decimals to Decimal Fractions
545
Step 1
545 1
Step 2
1 2
.54
Places
3
545 1000
Step 3
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Adding Decimals

• Add 7 5.3 24.139 .0003 5.02

7.0000 5.3000 24.1390 .0003 5.0200
41.4593
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Subtracting Decimals

• Subtract 45.3 - 15.273

45.300 - 15.273
30.027
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Multiplying Decimals
9.09 (2 decimal places) x 3.8 (1 decimal
places)
3 decimal places
34542
34.542
5 decimal places
17275
.17275
6.91 x .025
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Dividing Decimals
3 Steps 1. Make the divisor a whole number by
moving the decimal point to the right 2. Move
the decimal point in the dividend to the right
the same number of places as in step 1. If there
are not enough places, add zeros to the right of
the dividend. 3. Place the decimal point in the
quotient above the new decimal point in the
dividend. Divide as usual.
Example
4.5 82.89
45. 828.9
18.42
45. 828.90 45 378 360
189 180 90
90
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Decimals Applications in Foreign Currency
Key Currency Cross Rates
2 billion pounds x 1.7433 3.4866 3.49
Billion
Check 3.49 x .57360 2.001 2 Billion pounds
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Shortcuts for Multiples of 10
Multiplication

• Count the zeros in the multiplier
• Move the decimal point the same
• number of spaces to the right

68.9
6890
6.89 x 1000
6.89 x 10
6.89 x 100
689
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Shortcuts for Multiples of 10
Division

• Count the zeros in the divisor
• Move the decimal point the same
• number of spaces to the left

.689
.00689
6.89 / 1000
6.89 / 10
6.89 / 100
.0689