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Chapter 7: Problem 75

Convert \(8 / 3\) to a percent, and round your answer to the nearest tenth of a percent.

Short Answer

Expert verified
The result is approximately 266.7%.

Step by step solution

01

Divide the Numerator by the Denominator

First, perform the division of the fraction to convert it to a decimal. Divide 8 by 3 to obtain approximately 2.6667.
02

Convert Decimal to Percentage

To convert a decimal number to a percentage, multiply the decimal by 100. Thus, multiply 2.6667 by 100 to get 266.67.
03

Round to the Nearest Tenth of a Percent

Now that you have the percentage as 266.67%, round it to the nearest tenth place. So, 266.67% rounds to 266.7%.

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Key Concepts

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

Fractions to Decimals
Turning fractions into decimals is a straightforward process. It's all about dividing! For any fraction, take the top number (numerator) and divide it by the bottom number (denominator).
In our example, we have \(\frac{8}{3}\). Here, the numerator is 8, and the denominator is 3.
The act of division will transform the fraction into a decimal.
Consider these simple steps:
  • Take the numerator: 8
  • Take the denominator: 3
  • Perform the division: 8 divided by 3 gives you 2.6667
Dividing gives us the decimal representation of the fraction. Now, this decimal can be used in further calculations, such as converting into a percentage.
Rounding Decimals
Rounding is an important skill, especially when you're dealing with numbers that have many decimal places. Rounding to the nearest tenth means you are looking at the first place after the decimal point.
This step simplifies our numerical results. Here's how to round decimals properly:
  • Locate the tenths digit (first digit after the decimal point). In 266.67, it is 6.
  • Look at the digit one place to the right, in the hundredths spot. Here, it's 7.
  • If the hundredths digit is 5 or more, round the tenths digit up by one. If it's less than 5, keep the tenths digit the same.
For 266.67, since the hundredths digit is 7, the tenths digit (6) will round up to 7. This provides us with a rounded percentage of 266.7%.
Mathematical Division
Mathematical division is a fundamental concept in mathematics. It involves breaking a number (the dividend) into equal parts.
When you divide, you're essentially distributing the dividend into a number specified by the divisor. For example:
  • The dividend is 8,
  • The divisor is 3.
  • Performing the division gives 2 as a complete part and a repeated cycle of 0.6667.
Key points to remember are:
  • Each completed cycle contributes to the next digit in the decimal.
  • Division helps simplify complex numbers, like fractions, into a more workable form.
Understanding how to divide properly is crucial for converting fractions to decimals, and ultimately into percentages, as we've done in this exercise.

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Most popular questions from this chapter

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