Converting Metric Units With Decimals
Converting metric units with decimals means understanding that each metric unit is a power of 10 larger or smaller than the next. Since 1 meter equals 100 centimeters, each centimeter is 1/100 of a meter, or 0.01 m. So an object that is 25 cm long is also 0.25 m long — you simply divide by 100 or move the decimal two places to the left. Conversely, to go from meters to centimeters, multiply by 100. This skill is essential in 7th grade math and science and is covered in Saxon Math, Course 2.
Key Concepts
Property Since 1 meter equals 100 centimeters, each centimeter is $\frac{1}{100}$ of a meter, which can be written as $0.01$ m. An object 25 cm long is also 0.25 m long.
Examples A bookshelf is 75 cm tall. Since 1 cm is $0.01$ m, the bookshelf is $0.75$ meters tall. A student's desk is 1.45 meters wide. To convert to centimeters, we multiply by 100, so it is $145$ cm wide. A one foot ruler is about 305 mm long, which is the same as 30.5 cm or 0.305 m.
Explanation Changing metric units is like magic—just move the decimal! Since 100 centimeters make up one meter, any length in centimeters is just a 'part' of a whole meter. We write these hundredth parts using decimals, which makes converting between units a snap.
Common Questions
How do you convert centimeters to meters?
Divide the number of centimeters by 100 to get meters, since there are 100 centimeters in 1 meter. For example, 45 cm ÷ 100 = 0.45 m.
How do you convert meters to centimeters?
Multiply the number of meters by 100 to get centimeters. For example, 1.8 m × 100 = 180 cm.
Why does converting metric units involve moving decimal points?
The metric system is based on powers of 10, so converting between units is the same as multiplying or dividing by 10, 100, or 1000 — which is equivalent to moving the decimal point left or right.
What is the metric system?
The metric system is an international system of measurement based on powers of 10. Units include meters for length, grams for mass, and liters for volume, each with prefixes like kilo-, centi-, and milli- indicating the scale.
When do students learn metric unit conversions?
Metric unit conversions are typically taught in 6th and 7th grade math and science, building on an understanding of decimal operations.
What are common mistakes when converting metric units?
Common mistakes include multiplying instead of dividing (or vice versa) and moving the decimal point in the wrong direction. Remembering that ‘centi-’ means 1/100 helps avoid errors.
Which textbook covers converting metric units with decimals?
Saxon Math, Course 2 covers converting metric units with decimals.