# The Metric System Homework

## Session 3, Homework

Problem H1

1. The meter was originally based on the size of the Earth, with the distance from the equator to the North Pole being arbitrarily defined as 10 million m. What is another way to express the distance of 10 million m?
2. The Earth is not quite spherical, but for practical purposes we can think of Earth as having a circumference of 40 Mm. Thus, originally the meter was considered to be about 1/40,000,000 of Earth’s circumference. Use the Web or reference books to find out how a meter is officially defined today.

Problem H2

Match the metric quantities on the left with the approximate lengths/distances on the right:

 1 gigameter (1 • 109) A. distance a fast walker walks in 10 minutes 1 megameter (1 •106) B. size of an atom 1 kilometer (1 •103) C. waist height of an average adult 1 meter (base unit) D. size of bacteria 1 centimeter (1 •10-2) E. thickness of a dime 1 millimeter (1 •10-3) F. distance from Atlanta to Miami 1 micrometer (1 •10-6) G. width of a fingernail 1 picometer (1 •10-12) H. Earth’s distance from Saturn

Problem H3

A nickel is said to weigh 5 g. How much is 1 kg of nickels worth?

Problem H4

Give the approximate mass of the following volumes of water:

1. 6.5 L
2. 30 cm3
3. 18 mL
4. 12 m3

Problem H5

Why might a student be confused by this question: Which is more, 1.87 kg or 1,869 g? Explain.

The article “Do Your Students Measure Up Metrically?” points out some of the challenges of helping students in the United States learn the metric system. Discuss or think about how you might improve instruction on the metric system in your classroom or school.

Taylor, P. Mark; Simms, Ken; Kim, Ok-Kyeong; and Reys, Robert E. (January, 2001). Do Your Students Measure Up Metrically? Teaching Children Mathematics, 282-287.

Do Your Students Measure Up Metrically?

### Solutions

Problem H1

1. Ten million meters can also be expressed as 10,000 km, or 10 Mm.
2. A meter is defined to be the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second. In this way, it can be defined in terms of the second, another base unit of the metric system, and the constant speed of light.

Problem H2

• 1 gigameter – H. Earth’s distance from Saturn
• 1 megameter – F. distance from Atlanta to Miami
• 1 kilometer – A. distance a fast walker walks in 10 minutes
• 1 meter – C. waist height of an average adult
• 1 centimeter – G. width of a fingernail
• 1 millimeter – E. thickness of a dime
• 1 micrometer – D. size of bacteria
• 1 picometer – B. size of an atom

Problem H3

Since it takes 1,000 g to make a kilogram, there are about 200 nickels in a kilogram. Two hundred nickels are worth \$10.

Problem H4

1. The mass is approximately 6.5 kg.
2. Since 1 cm3 is equivalent to 1 g, 30 cm3 of water has a mass of 30 g.
3. Since 1 mL is equivalent to 1 g, 18 mL has a mass of 18 g.
4. Twelve cubic meters is equivalent to 12,000 dm3. Since 1 dm3 of water has a mass of 1 kg, 12 m3 has a mass of 12,000 kg.

Problem H5

In terms of the number of units, 1,869 is a much larger number, so a student might be confused and say that 1,869 g is more. But since a kilogram is equivalent to 1,000 g, 1.87 kg is actually 1,870 g, which is more. This confusion might disappear once the student is more familiar with the metric system, which makes this type of conversion much easier than converting, say, inches to miles.