Problem 31 Complete. Do as much as possible... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 8: Problem 31

Complete. Do as much as possible mentally. 0.024 mm =_______ m

Short Answer

Expert verified

0.000024 m

Step by step solution

Understand the Metric Conversion

Know that 1 millimeter (mm) is equal to 0.001 meters (m). This is because 'milli-' means one-thousandth.

Set Up the Conversion

Multiply the given value in millimeters by the conversion factor to convert it to meters. So, 0.024 mm * 0.001 m/mm.

Perform the Multiplication

Calculate the result of 0.024 * 0.001. This can be done mentally as shifting the decimal point three places to the left.

Write the Final Answer

After calculating, 0.024 mm is equal to 0.000024 m.

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Key Concepts

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

millimeters to meters

To convert millimeters (mm) to meters (m), it's essential to understand the metric system. The prefix 'milli-' means one-thousandth. This means that 1 millimeter is one-thousandth of a meter. Therefore, the conversion factor from millimeters to meters is 0.001.
So, when you need to change a measurement in millimeters to meters, you multiply the number of millimeters by 0.001. This is a straightforward calculation that can often be done mentally or with simple multiplication.

multiplication

Multiplication is a fundamental arithmetic operation that involves finding the product of two numbers. In metric conversion, you often multiply the given measurement by a conversion factor to change from one unit to another.
For example, in our exercise, we multiply the given value in millimeters (0.024 mm) by the conversion factor (0.001 m/mm). This multiplication helps us scale down the measurement from millimeters to meters.
Performing the multiplication: \[ 0.024 \times 0.001 = 0.000024 \] involves simple movement of the decimal point (which we will discuss next). The product tells us that 0.024 millimeters is equal to 0.000024 meters.

decimal point

The decimal point is crucial in understanding the conversion. It separates the whole number part from the fractional part of a number. In our exercise, we need to shift the decimal point to multiply by 0.001.
Shifting the decimal point three places to the left makes the calculation straightforward: 0.024 becomes 0.000024.

First, consider the original number: 0.024

Shift the decimal point three places to the left since you are multiplying by 0.001:

0.024 -> 0.0024 -> 0.00024 -> 0.000024
By understanding the decimal point movement, you can easily and mentally convert units without needing a calculator.

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91影视

Complete. Do as much as possible mentally. 0.024 mm =_______ m

Short Answer

Step by step solution

Understand the Metric Conversion

Set Up the Conversion

Perform the Multiplication

Write the Final Answer

Key Concepts

millimeters to meters

multiplication

decimal point

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