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Learning Math Home
Measurement Session 3: Solutions
Session 3 Part A Part B Homework
Measurement Site Map
Session 3 Materials:

A B 


Solutions for Session 3, Part A

See solutions for Problems: A1 | A2 | A3 | A4 | A5 | A6


Problem A1

Answers will vary. Some of the common measurements are the meter, the liter, and the gram. Most people associate the number 10 with the metric system, since relationships in this system are determined by powers of 10.

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Problem A2

Most countries use the metric system because it is an international standard; it makes it easy for different countries to talk about the same units of length or mass. The metric system is also designed for easy calculation.

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Problem A3


There are many patterns in the table that you may want to discuss. First, the metric system uses prefixes in front of a unit name as a multiplying factor. Most prefixes multiply or divide units in steps of 1,000 as you go up and down the table.


The more commonly used prefixes are those from 10-3 to 103. These units are commonly used when measuring areas, volumes, and lengths. Throughout this session, you should focus on gaining familiarity with those particular prefixes.


A centimeter is a 100th of a meter (1 m = 100 cm). A millimeter is a 1,000th of a meter (1 m = 1,000 mm). A kilometer is 1,000 m (1,000 m = 1 km). A micrometer is a millionth of a meter (1 m = 1,000 000 Ám).


These measurements are related because they are all built on powers of 10, with the meter as the base unit. The prefix tells you how many meters (or how much of a meter) you're talking about.


A centimeter could be 10 mm or 0.01 m. A millimeter could be 0.1 cm or 0.001 m. A decimeter could be 10 cm, 100 mm, 0.1 m. Other answers are also possible!

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Problem A4

One primary reason is that a number written in metric units can easily be converted by multiplying or dividing by powers of 10, since this type of multiplication is done by moving the decimal point. For example, 2.54 cm is equivalent to 25.4 mm and 0.0254 m. Each of these conversions is done by knowing the power of 10 associated with the conversion and moving the decimal point by that many places.

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Problem A5


As 1,000 m is 1 km, 3,600 m is 3.6 km. We simply moved the decimal point three places to the left.


Since 0.001 m is 1 mm, 0.028 m is 28 mm. Again, we just moved the decimal point three places to the right.


One way is to convert the millimeters to meters and then to kilometers: 1,000 mm equals 1 m, so 4,600,000 mm equals 4,600 m. Similarly, 1,000 m equals 1 km, so 4,600 m equals 4.6 km (i.e., we moved the decimal point six places to the left).

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Problem A6

To make a fair comparison, we must first convert gigameters to megameters (or vice versa). Since 1 Gm = 1,000 Mm, the Sun's distance from the Earth is 150 • 1,000, or 150,000 Mm. The ratio is now 150,000:384, or about 390 times farther away.

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