/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 23 Express each fraction as a perce... [FREE SOLUTION] | 91影视

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Chapter 12: Problem 23

Express each fraction as a percent. $$\frac{5}{6}$$

Short Answer

Expert verified
The fraction \( \frac{5}{6} \) is approximately \( 83.33\% \).

Step by step solution

01

Understand the Problem

We need to convert the fraction \( \frac{5}{6} \) into a percentage. To do this, we'll first convert the fraction to a decimal and then convert that decimal to a percentage.
02

Convert the Fraction to a Decimal

Divide the numerator by the denominator to convert the fraction to a decimal. \[ \frac{5}{6} = 0.8333\overline{3} \] This means \( \frac{5}{6} \) is approximately \( 0.8333 \).
03

Convert the Decimal to a Percentage

To convert a decimal to a percentage, multiply by 100. \[ 0.8333 \times 100 = 83.33 \] This means the percentage equivalent of \( \frac{5}{6} \) is approximately \( 83.33\% \).

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Key Concepts

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

Converting Fractions
Converting fractions can sometimes seem daunting, but it becomes simple once you understand the steps. A fraction is essentially a division. The numerator (top number) is divided by the denominator (bottom number). For example, in the fraction \(\frac{5}{6}\), 5 is the numerator and 6 is the denominator. To convert a fraction into a more familiar form, we can change it into a decimal. This gives us a clearer understanding of the fraction's value in relation to whole numbers. Begin by dividing 5 by 6, which will transform the fraction into a decimal number.
Decimal Conversion
Once you have a fraction, the next step is to convert it into a decimal. A decimal is another way to represent values that are not whole numbers. To convert \(\frac{5}{6}\) into a decimal, you perform the division: 5 divided by 6. The result of this division is a repeating decimal: \(0.8333\overline{3}\). This indicates that the decimal equivalent of \(\frac{5}{6}\) is \(0.8333\), where the 3 repeats indefinitely. Understanding decimal conversion is crucial because it bridges fractions and percentages.
Percentage Conversion
After the fraction is converted to a decimal, the final step is turning it into a percentage. A percentage is a way to express a number as a part of 100, making it easier to compare different quantities. To convert from a decimal to a percentage, you simply multiply the decimal by 100. For \(0.8333\), this calculation would be \(0.8333 \times 100 = 83.33\). Thus, the fraction \(\frac{5}{6}\) is approximately \(83.33\%\). Remember, multiplying by 100 is the key action because it shifts the decimal point two places to the right.

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Most popular questions from this chapter

Use the set of data \(\\{2.4,2.1,4.8,2.7,5.5,1.4,3.9\\}\). $$\text { Solve }-5 a-6=24$$

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