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Chapter 7: Problem 57

Convert the fraction to a percent. $$\frac{7}{8}$$

Short Answer

Expert verified
87.5%

Step by step solution

01

Divide the numerator by the denominator

To convert the fraction \(\frac{7}{8}\) into a percent, first divide the numerator (7) by the denominator (8). \(\frac{7}{8} = 0.875\)
02

Multiply by 100

Next, multiply the result from Step 1 by 100 to convert the decimal into a percent. \((0.875 \times 100 = 87.5)\)
03

Write the final answer

The fraction \(\frac{7}{8}\) as a percent is 87.5%.

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Key Concepts

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

Understanding Numerator and Denominator
In any fraction, like \(\frac{7}{8}\), it consists of a numerator and a denominator. The numerator is the top number, which is 7 in this example. It represents a part of the whole.

The denominator is the bottom number, which in this case is 8. It indicates into how many parts the whole is divided.

Understanding these two components is the first step when you are working on converting a fraction into another form, such as a decimal or a percent.
By dividing the numerator by the denominator, you break down the fraction into a more manageable form.
Decimal Conversion
Decimal conversion involves turning the fraction into its decimal form. This step makes it easier to convert the fraction to a percent.

To convert the fraction \(\frac{7}{8}\) into a decimal, you simply divide 7 by 8.
Using a calculator or doing it manually, 7 divided by 8 equals 0.875.

Therefore, \(\frac{7}{8}\) converts to 0.875 in decimal form.
Decimals are necessary when converting fractions to percentages, as the conversion process involves multiplying the decimal by 100.
Percent Calculation
After converting the fraction to a decimal, the next step is to find the percent.

The percent is found by taking your decimal value and multiplying it by 100.
In our example, the decimal value of \(\frac{7}{8}\) is 0.875.

When you multiply 0.875 by 100, you get 87.5.

Hence, \(\frac{7}{8}\) as a percentage is 87.5%.

Remember, multiplying by 100 moves the decimal point two places to the right, effectively converting the decimal into a percent.

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Most popular questions from this chapter

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