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Chapter 7: Problem 70

Convert \(5 / 3\) to a percent, and round your answer to the nearest hundredth of a percent.

Short Answer

Expert verified
The fraction \( \frac{5}{3} \) is approximately \(166.67\%\) when converted to a percent.

Step by step solution

01

Understand the Fraction to Percent Conversion

To convert a fraction to a percent, multiply the fraction by 100. In this case, we have \( \frac{5}{3} \). Thus, we need to calculate: \( \left( \frac{5}{3} \right) \times 100 \).
02

Perform the Multiplication

Multiply \( \frac{5}{3} \) by 100 to find the percentage. This calculation is: \( \left( \frac{5}{3} \right) \times 100 = \frac{5 \times 100}{3} = \frac{500}{3} \).
03

Simplify the Fraction to a Decimal

Divide 500 by 3 to convert the fraction to a decimal. This gives \( \frac{500}{3} = 166.6666\ldots \). The repeating decimal can be approximated as \(166.67\) when rounding to the nearest hundredth.
04

Format the Decimal as a Percent

The result from Step 3 represents the percentage value. Since we need a percentage to two decimal places, the final percent is \(166.67\%\).

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Key Concepts

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

Multiplying Fractions
Multiplying fractions is a simple and straightforward process. When you multiply fractions, you just need to multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. Let's consider the example of multiplying \( \frac{5}{3} \). To convert this fraction into a percentage, you multiply it by 100, since percentages are parts out of 100. This is how we calculate the percentage of a given fraction:
  • Take the numerator of your fraction. In this case, it's 5.
  • Take the denominator of your fraction. Here, it's 3.
  • Multiply the numerator by 100 and divide this result by the denominator: \( \frac{5 \times 100}{3} \).
This multiplication gives you \( \frac{500}{3} \), which leads you to solving for a decimal. Multiplying fractions like this is crucial in turning them into percentages, allowing you to express the fraction as a part of 100.
Rounding Decimals
Rounding decimals involves choosing a certain number of decimal places to approximate the value of your number. In this exercise, the decimal produced from \( \frac{500}{3} \) is \(166.6666\ldots\) and goes on infinitely. We need to round this to the nearest hundredth for simplicity and precise representation.
  • Identify the hundredth position in your decimal. In \(166.6666\ldots\), this is the second digit after the decimal point, which is 6.
  • Look at the next number to the right (the thousandth position). If it's 5 or more, you round up the hundredth position by 1. Here, it's 6, so we round the hundredths place up, changing it from 66 to 67.
This makes our rounded decimal \(166.67\). Rounding like this helps in making numbers more manageable and is often necessary when working with percentages in math and everyday life.
Converting Fractions to Decimals
Converting fractions to decimals can be done by dividing the numerator by the denominator. This conversion is part of turning the fraction into a simpler form:
  • Take the example \( \frac{500}{3} \) from the previous step, which we need to simplify into a decimal.
  • Perform the division: 500 divided by 3 gives you approximately \(166.6666\ldots\).
After converting the fraction into a long decimal, you round it to the desired precision, which, in this case, is to the nearest hundredth: \(166.67\). Converting fractions to decimals simply entails division, and this process is foundational for many mathematical conversions, including converting to percentages.

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