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# Racing for Significant Figures

By Shana McAlexander
Product Manager

### Overview

This kinesthetic activity helps students grasp the difficult concept of significant figures. Student groups compete with each other to generate answers to questions about significant figures (also called significant digits). Each student holds a card with a single digit (0 to 9), decimal, or negative sign. Students organize themselves so that their cards show the correct answers.

### Content standards

This activity is appropriate for middle and high school students and addresses the following National Science Education Standard:

• Grades K–12, Unifying Concepts and Processes: Constancy, Change, and Measurement

### Background

Measurement values are only as accurate as the measurement equipment used to collect them. For example, measuring meters with a meter stick is rather accurate; measuring millimeters (1/1,000 of a meter) with a meter stick is inaccurate. Using significant figures helps prevent the reporting of measured values that the measurement equipment is not capable of determining. A significant figure is comprised of the fewest digits capable of expressing a measured value without losing accuracy. As the sensitivity of the measurement equipment increases, so does the number of significant figures. Knowing the rules for working with significant figures can help your students. “Rounding” numbers is the usual method of achieving significant figures. Once the appropriate number of significant figures for any measurement, calculation, or equation is determined, students can practice rounding their answers appropriately.

### Rules governing significant figures

#### Basic rules

1. Any non-zero digit is significant.
2. Zeros between non-zero digits are always significant.
Example: 3,606 has 4 significant figures.
3. Zeros that indicate the decimal point are not significant.
Example: 360,600 has 4 significant figures.
4. Zeros following a decimal are significant.
Example: 3.60 has 3 significant figures but 3.6 has 2.
5. Zeros appearing before a non-zero digit are not significant.
Example: 0.009 only has 1 significant figure.

The number of significant figures in a sum or difference is equal to that of the least accurate measurement in the equation. The answer must contain the same number of decimal places as the least accurate measurement.

Example: Without using significant figures: 606.02 – 65.3 = 540.72

Using significant figures: 540.7

#### Multiplication and division rule

The number of significant figures in a product or quotient is equal to that of the least accurate measurement in the equation. The answer must contain the same number of significant figures as the least accurate measurement.

Example: Without using significant figures: 606.02 × 63 = 38,179.26

Using significant figures: 38,000 (has only 2 significant figures)

#### Materials

• Blank Paper or Card Stock (11 for each group)
• Thick Marking Pen
• Calculators (optional)
• Measuring Equipment (to use as examples)

#### Pre-activity (teacher)

• Determine the number of groups in your class.
• Assemble 11 sheets of paper or card stock to make up a set for each group.
• On each sheet of paper in a set, write 1 value (0 to 9), a decimal point, or a negative sign.

#### Procedure (teacher)

1. Provide an overview of significant figures. Review the significant figure rules presented in the background section. Display examples of measuring equipment with variations of sensitivity.
2. Organize student groups and distribute 1 set of numbers to each group.
3. Facilitate or assign a student to facilitate each level of the games.
4. Award points for correct answers.
5. Have fun with the Significant Figure Race.

### Significant figure race

#### Level 1

1. The facilitator asks basic significant figure questions.
2. Students race to get in place and hold up cards that form the correct answers.
Example questions:
1. How many significant figures are in 1,500?
2. How many significant figures are in 1,500.01?
3. How many decimal places are in 2.234?
Answer: 3 (This concept is useful for addition and subtraction questions later in this activity.)

#### Level 2

Example questions:
1. Which number is less accurate: 301 or 3.01?
2. What is 60 + 83.2, using significant figures?
3. What is 0.158 + 0.4, using significant figures?
4. What is 0.11 – 2.2, using significant figures?

#### Level 3

1. The facilitator asks multiplication or division questions.
Example questions:
1. What is 63.4 × 151, using significant figures?