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Chapter 7: Problem 22

Change each decimal to a percent. $$0.34$$

Short Answer

Expert verified
0.34 as a percent is 34%.

Step by step solution

01

Understanding the Concept

To convert a decimal to a percent, we need to understand that a percent represents a number out of 100. This means we take the decimal and adjust it so that it fits this 'out of 100' requirement.
02

Transforming the Decimal

Convert the decimal to a percent by multiplying it by 100. This changes the scale of the number from being out of 1 to being out of 100. For our decimal of 0.34, we do the following calculation: \(0.34 \times 100\).
03

Calculating the Result

Carry out the multiplication from the previous step. Therefore, \(0.34 \times 100 = 34\). This gives us the number as a percent.
04

Applying the Percent Symbol

After calculating the result, we need to include the percent sign (%) to indicate that we have converted the decimal into a percent. The final answer is 34%.

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Key Concepts

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

Percent
Understanding the concept of a percent is essential when dealing with conversions. A percent is a way to express a number as a fraction of 100. Instead of handling large numbers, we reduce or magnify them to fit within a 0 to 100 scale.
This makes comparison and comprehension easier across various applications, like calculating discounts or comparing success rates in experiments.
By definition, 1% is equivalent to 1 out of 100, or in decimal form, 0.01. Hence, converting numbers into percent form is helpful in numerous practical scenarios.
Decimal Multiplication
At the core of converting a decimal to a percent lies the process of decimal multiplication. This calculation stretches the decimal to fit into the percent format.
To perform this operation, simply multiply the decimal number by 100.
  • The decimal represents a part of a whole, or out of 1.
  • By multiplying by 100, you change its domain from out of 1 to out of 100.
  • For instance, with our example of 0.34, the multiplication step looks like this: \(0.34 \times 100 = 34\).
Through this multiplication, we scale the decimal to its equivalent percent.
Mathematical Conversion Steps
Converting decimals to percents involves a series of straightforward calculation steps, making the process simple and repeatable.
Here's a breakdown of these steps:
  • Step 1: Recognize that a percent means "per hundred," so identify your decimal.
  • Step 2: Multiply the decimal by 100 to adjust its scale from a base of one to a base of hundred.
  • Step 3: Perform the multiplication to get the numeric result.
  • Step 4: Add the percent sign (%) to denote that the number is now a percentage.
By following these steps, you can successfully convert any decimal into a percent!
Percent Sign
Once you've calculated the decimal-to-percent conversion, the final step is to apply the percent sign (%). This symbol is crucial as it signals that the number is now a percentage.
Including the percent sign transforms your numeric result into a clear and universally understood format.
For the example decimal of 0.34, after converting it to 34, adding the percent sign gives us 34%.
The percent sign is a small yet important detail that ensures effective communication of the mathematical conversion.

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Most popular questions from this chapter

Write as a percent. Write the remainder in fractional form. $$2 \frac{5}{8}$$

Write as a decimal. $$\frac{3}{16}$$

Divide. $$0.125 \div 0.0625$$

Divide. Round the answers to the nearest thousandth, if necessary. $$\frac{21}{42}$$

Divide. Round the answers to the nearest thousandth, if necessary. $$\frac{31.9}{78}$$
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