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Chapter 8: Problem 5

Complete. Do as much as possible mentally. a) 1 cm = ______m b) 1 m = ______cm

Short Answer

Expert verified
a) 0.01 m, b) 100 cm

Step by step solution

01

Understand the Conversion Factor

There are 100 centimeters (cm) in one meter (m). This means 1 m = 100 cm and 1 cm = 0.01 m.
02

Solve Part (a)

To convert 1 cm to meters, use the relationship that 1 cm = 0.01 meters. Therefore, 1 cm = 0.01 m.
03

Solve Part (b)

To convert 1 m to centimeters, use the relationship that 1 meter = 100 centimeters. Therefore, 1 m = 100 cm.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

centimeters to meters
When converting from centimeters to meters, you need to understand that there are 100 centimeters in one meter. This means one centimeter is a fraction of a meter. Specifically, 1 centimeter (cm) is equal to 0.01 meters (m). The conversion factor here is 0.01.
For example:
  • If you have 50 cm, you multiply by the conversion factor: 50 cm * 0.01 = 0.5 m
  • If you have 250 cm, you use the same method: 250 cm * 0.01 = 2.5 m
Understanding this is crucial for accurate measurements and calculations.
meters to centimeters
On the other hand, to convert meters to centimeters, you use the fact that there are 100 centimeters in one meter. So, 1 meter is equal to 100 centimeters. This conversion factor is 100.
Let's consider some examples:
  • For 2 meters, you would calculate: 2 m * 100 = 200 cm
  • If you have 0.75 meters, the calculation is: 0.75 m * 100 = 75 cm
Quick mental conversions often rely on understanding these fundamental relationships.
conversion factors
Conversion factors are numbers used to change one unit of measurement into another by multiplying or dividing. In the context of metric conversions between centimeters and meters, the conversion factors are based on the relationship that 1 meter = 100 centimeters.
Here are some key points:
  • To convert from cm to m: Use the factor 0.01. Multiply the number of centimeters by 0.01 to get the measurement in meters. For instance, 150 cm * 0.01 = 1.5 m.
  • To convert from m to cm: Use the factor 100. Multiply the number of meters by 100 to get the measurement in centimeters. For example, 3.4 m * 100 = 340 cm.
Remember, accurate conversions depend on using the correct conversion factor for the units you are working with.

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