75
The rules for calculating with significant figures and scientific notation are given in your
textbook. For complete instructions on using your calculator, CONSULT THE MANUAL
THAT CAME WITH YOUR CALCULATOR.
EXERCISES:
A. Indicate whether each of the following is a measured or an exact quantity.
5 books
exact
12 roses
exact
5 lb
measured
16 ounces in 1 pound
exact
9.25 g
measured
361 miles
measured
0.035 kg
measured
1000 m in 1 km
exact
B. Write the following numbers in scientific notation.
4,450,000 (4 sig figs)
4.450×106
0.00032
3.2×10-4
38,000 (2 sig figs)
3.8×104
25.2
2.52×101
0.0000000021
2.1×10-9
0.0505
5.05×10-2
Write the following as standard decimal numbers.
4.09 × 102
409
3 × 10-4
0.0003
5.315 × 101
53.15
8.2 × 10-3
0.0082
3.156 × 103
3156
2.46 × 10-6
0.00000246
C. State the number of significant figures in each of the following measurements.
4.5 m
2
204.25 g
5
0.0004 L
1
6.25 × 105 mm
3
805 lb
3
34.80 km
4
2.50 × 10-3 L
3
8 × 105 g
1
Chapter 2
76
D. Round off each of the following to the number of significant figures indicated. Put the
number in scientific notation if needed to avoid writing an ambiguous number.
Three significant figures
Two significant figures
0.4108
0.411
0.41
143.63212
144
1.4×102
532,800
5.33×105
5.448 × 102
5.45×102
0.00858345
0.00858
5.3×105
5.4×102
0.0086
E. Perform the following multiplication and division calculations. Give a final answer with the
correct number of significant figures.
4.5 × 0.28
1.3
0.1184 × 8.00 × 0.0345
0.0327
(2.5 × 104) × (5.0 × 10-7)
0.013
(42.4)(15.6)
5.23
1.265 × 10 2
(35.56)(1.45)
(4.8 × 10−1 )(0.56)
1.9×102
F. Perform the following addition and subtraction calculations. Give a final answer with the
correct number of significant figures.
13.45 mL + 0.4552 mL
13.91 mL
145.5 m + 86.58 m + 1045 m
1277 m
1315 + (2.0 × 102) + (1.10 × 103)
2.62×103
245.625 g - 80.2 g
165.4 g
4.62 cm - 0.855 cm
3.76 cm
G. Mixed operations.
Chapter 2
77
(12.6 + 0.57)/3.1415
4.19
(13.54 × 1.56) + (22.6 ÷ 3.5)
27.6
(15.4 + 3.45)
(44.65 − 23.6)
30.0
33.5 ×
H. Problems
1. A number that counts something is an exact number. When you say 4 mugs, 5 books, or 2
watches, you are using exact numbers. However, when you use a rule to measure the height
of your friend as 155.2 cm, you obtain a measured number. Why are some numbers called
exact while other numbers are called measured?
Exact numbers are defined numbers or counted numbers and no digits are estimated.
Measured numbers come from measurements and the last digit is an estimate.
2. In what place (ones, tens, tenths, etc.) is the estimated digit in each of the following
measurements.
1.5 cm
tenths
4.50 × 103 mi
tens
0.0782 m
ten-thousandths
42.50 g
hundredths
3. Bill and Beverly have measured the sides of a rectangle. Each recorded the length of the
rectangle as 6.7 cm and the width as 3.9 cm. When Bill calculates the area (by multiplying
the length by the width), he gives an answer of 26.13 cm2. However, Beverly correctly
records her answer for the area as 26 cm2.
(a) Why is there a difference between the two answers when both students used the same
measurements?
Bill did not follow the sig fig rules
(b) You are going to tutor Bill. What would you tell him to help him correct his answer?
The answer cannot have more sig figs than the least number of sig figs you originally
have.
I. Activity
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78
List at least eight numbers (and units) you might use throughout the day (such as measurements,
prices, definitions, cooking quantities, gas purchases, prescription dosages, etc.). Identify each
number as exact or measured and explain why it is exact or measured. Did you use a measuring
tool? Did you count out something? Did you use a definition?
Number used
Type of number
(exact or measured)
Explanation
____________________
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______________________
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______________________
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______________________
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Additional Study Problems
1. How many significant figures are in each of the following numbers?
20.03
4
0.0094
2
53.000
5
2.474×10-3
4
2. Convert each of the following decimal numbers to scientific notation retaining the correct
number of significant figures.
300.4
3.004×102
0.0059301
5.9301×10-3
0.0000003
3.×10-7
3. Convert each of the following numbers to standard decimal notation retaining the correct
number of significant figures.
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79
7.653 × 102
765.3
8.00 × 10-3
0.00800
3.006 × 10-1
0.3006
4. Do the following calculations and express your answer using the correct number of significant
figures.
1234.7 + 7 - 3.25 = 1238
4.35 × 103 + 7.966 × 102 = 5.15×103
11.45 × 2.3
2.00 × 0.0345
2.330 − 1.2
3.444
= 3.8×102
= 0.33
(2.45 × 10-3)(5.0 × 102) = 1.2
Chapter 2