Significant Figures

1
Significant Figures

• SPH3U

2

• Precision How well a group of measurements made
  of the same object, under the same conditions,
  actually agree with one another.
• These points are precise with one another but not
  accurate.

3

• Accuracy represents the closeness of a
  measurement to the true value.
• Ex the bulls-eye would be the true value, so
  these points are accurate.

4
Why Significant Figures?

• Precision is determined by the instrument we use
  to take measurements. So, our calculations must
  be only as precise as the measurements.
• NOTE The last digit of any measurement is always
  a guess therefore it is uncertain.

5
Measuring precision
6
Other instruments
7
Rounding

• You will need to round off sig. figs when you
  multiply, divide, add or subtract.
• When rounding off to a certain place value, you
  need to look one place farther.
• If the next digit is a 5 or higher, you round the
  digit before it UP.
• If the next digit is a 4 or lower, you DONT
  round up.

8
Using sig figs The Rules!

• Digits from 1-9 are always significant.
• Zeros between two other significant digits are
  always significant
• Zeros at the beginning of a number are never
  significant.
• Zeros at the end of a number are only significant
  IF there is a decimal place.

9
Example Number of sig figs Why?
453kg 3 All non-zero digits are always significant.
5057L 4 Zeros between 2 sig. dig. are significant.
5.00 3 Additional zeros to the right of decimal and a sig. dig. are significant.
0.007 1 Placeholders are not sig.
10

• Problems Indicate the number of significant
  figures...
• 1. 1.235 ______
• 2. 2.90 ______
• 3. 0.0987 ______
• 4. 0.450 ______
• 5. 5.00 ______
• 6. 2300 ______
• 7. 230 ______
• 8. 230.0 ______
• 9. 9870345 ______
• 10. 1.00000 ______

11

• 1. 1.235 ___4___
• 2. 2.90 ___3___
• 3. 0.0987 ___3___
• 4. 0.450 ___3___
• 5. 5.00 ___3___
• 6. 2300 ___2___
• 7. 230 ___2___
• 8. 230.0 ___4___
• 9. 9870345 ___7___
• 10. 1.00000 ___6___

12
Round these numbers to 3 significant figures

• 5.8746 ___________
• 8008 _____________
• 24.567 _________
• 100.04 __________
• 5634.3999 ____________
• 1.675 x 103 ____________

13

• 5.8746 __5.87_________
• 8008 ___8010__________
• 24.567 __24.6_______
• 100.04 ___100._______
• 5634.3999 __5630__________
• 1.675 x 103 ___1.68 x 103 _____

14
Multiplying and Dividing

• RULE your answer may only show as many
  significant figures as the multiplied or divided
  measurement showing the least number of
  significant digits.
• Example 22.37 cm x 3.10 cm 69.3
• (only 3 sig figs allowed)

15
Multiplying and Dividing Practice

• 1. 42.3 x 2.61 ______
• 2. 32.99 x 0.23 ______
• 3. 46.1 1.21 ______
• 4. 23.3 4.1 ______
• 5. 0.61 x 42.1 ______
• 6. 47.2 x 0.02 ______
• 7. 47.2 0.023 ______
• 8. 100 x 23 ______
• 9. 124 0.12 ______
• 10. 120 x 12 12.5 ______

16

• 1. 42.3 x 2.61 __110.____
• 2. 32.99 x 0.23 __7.6____
• 3. 46.1 1.21 __38.1____
• 4. 23.3 4.1 __5.7____
• 5. 0.61 x 42.1 __26____
• 6. 47.2 x 0.02 __0.9____
• 7. 47.2 0.023 __2100____
• 8. 100 x 23 __2000____
• 9. 124 0.12 __1000____
• 10. 120 x 12 12.5 __110____

17
Adding and Subtracting

• RULE your answer can only show as many place
  values as the measurement having the fewest
  number of decimal places.
• Example
• 3.76 g 14.83 g 2.1 g 20.7 g
• 3.76 is precise to the hundredths place, 14.83 is
  precise to the hundredths place, 2.1 is only
  precise to the tenths place, so we round off the
  final answer to the tenths place.

18
Adding and Subtracting Practice

• 1. 2.634 0.02 ______
• 2. 2.634 - 0.02 ______
• 3. 230 50.0 ______
• 4. 0.034 1.00 ______
• 5. 4.56 - 0.34 ______
• 6. 3.09 - 2.0 ______
• 7. 349 34.09 ______
• 8. 234 - 0.98 ______
• 9. 238 0.98 ______
• 10. 123.98 0.54 - 2.3 ______

19

• 1. 2.634 0.02 __2.65____
• 2. 2.634 - 0.02 __2.61____
• 3. 230 50.0 __280____
• 4. 0.034 1.00 __1.03____
• 5. 4.56 - 0.34 __4.22____
• 6. 3.09 - 2.0 __1.1____
• 7. 349 34.09 __383____
• 8. 234 - 0.98 __233____
• 9. 238 0.98 __239____
• 10. 123.98 0.54 - 2.3 __122.2____

20
Scientific Notation
21
Scientific Notation

• Scientists have developed a shorter method to
  express very large numbers.
• Scientific Notation is based on powers of the
  base number 10.

22

• 123,000,000,000 in s.n. is 1.23 x 1011
• The first number 1.23 is called the coefficient.
  It must be between 1 - 9.99
• The second number is called the base . The base
  number 10 is always written in exponent form. In
  the number 1.23 x 1011 the number 11 is referred
  to as the exponent or power of ten.

23
To write a small number in s.n.ex 0.00064

• First move the decimal after the first real
  number and drop the zeroes. Ex 6.4
• Next, count the number of places moved from the
  original decimal spot to the new decimal spot.
  Ex 4
• Numbers less than 1 will have a negative
  exponent. Ex -4
• Finally, put it together. Ex 6.4 x 10-4

24
Scientific Notation Practice

• 0.0826 _______________
• 2 630 000 _______________
• 945 000 _______________
• 1 760 000 _______________
• 0.00507 _______________
• 1.23 x 10-4 _______________
• 7.51 x 105 _______________
• 3.09 x 10-3 _______________
• 2.91 x 102 _______________
• 9.6 x 104 _______________

25

• 0.0826 __8.26 x 10-2___
• 2 630 000 __2.63 x 106___
• 945 000 __9.45 x 105___
• 1 760 000 __1.76 x 106___
• 0.00507 __5.07 x 10-3___
• 1.23 x 10-4 __0.000123_____
• 7.51 x 105 __751000______
• 3.09 x 10-3 __0.00309_____
• 2.91 x 102 __291_________
• 9.6 x 104 __96000_______