A measurement has three parts

Part 1:  A number read off an instrument such as a scale or ruler.

Part 2:  A unit for the number that is particular to each measurement.

Part 3:  A statement of the measurement's accuracy expressed in significant figures.

The significant figures rules are:

Rule #1: All non-zero digits are significant.

Rule #2: Zeros in front of a number are not significant.

Rule #3: Zeros between non-zero digits are significant.

Rule #4: Zeros at the end of a number are significant if there is a decimal point in the number.

Example

0.0203  has 3 significant figures

2.50 has 3 significant figures

2500 has 2 significant figures

3.7 x 10⁹ has 2 significant figures

45009 has 5 significant figures

100. has 3 significant figures

Significant figures in additions and subtractions

Decimal places are overwriting the significant figure rule. The answer should have the same number of decimal places as the quantity with the least decimal places.

Example

3.7 m + 9.40 m = 13.1 m

2.35 L + 1.2 L = 3.6 L

3.67 kg + 12.498 kg = 16.17 kg

Significant figures in multiplications and divisions

The product or quotient should have the same number of significant digits as the quantity with least significant figures.

Example

(0.023 m) x (3.40 m) = 0.078 m²

56.90 s / 2.45 s  = 23.2

TEST YOUR UNDERSTANDING

1. Which measurement contains a total of three significant figures?   (1) 0.12            (2) 012           (3) 120              (4) 120.

2. What is the product of (2.324 cm x 1.11 cm) expressed to the correct number of significant figures?

(1) 2.58 cm²          (2) 2.5780 cm²            (3) 2.5796 cm²      (4) 2.57964 cm²

3. Which quantity expresses the sum of the given masses to the correct number of significant figures?         22.1 g + 375.66 g + 5400.132 g

            1. 5800 g         2. 5798 g         3. 5797.9 g      4. 5797.892 g

4. Which mass measurement contains a total of three significant figures?     1. 22.0 g          2. 22.00 g        3. 220 g           4. 2200 g

5. The diagram shows a portion of a burette. What is the meniscus reading in milliliters?

            1. 16.00           2. 16.40           3. 17.00           4. 17.60

6. Which measurement contains three significant figures?     1. 0.08 cm    2. 0.080 cm       3. 800 cm     4. 8.08 cm

7. Given: (52.6 cm)(1.214 cm). What is the product expressed to the correct number of significant figures?    1. 64 cm²      2. 63.9 cm²     3. 63.86 cm²   4. 63.8564 cm²

6/02

Which mass measurement contains four significant figures?

            (1) 0.086 g         (2) 0.431 g      (3) 1003 g      (4) 3870 g

6/02

The diagram below represents a portion of a 100-milliliter graduated cylinder. What is the reading of the meniscus?

 (1) 35.0 mL           (2) 36.0 mL            (3) 44.0 mL      (4) 45.0 mL

8/04

50 A student calculates the density of an unknown solid. The mass is 10.04 grams, and the volume is 8.21 cubic centimeters. How many significant figures should appear in the final answer? (1)1 (2) 2 (3) 3 (4) 4

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