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Chapter 7: Problem 73

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{13}{15}$$

Short Answer

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Step by step solution

01

- Convert the fraction to a decimal

Divide the numerator (13) by the denominator (15). \(\frac{13}{15} = 0.8667\)
02

- Convert the decimal to a percentage

Multiply the decimal value by 100 to convert it to a percentage. 0.8667 \( \times \, 100 = 86.67\)
03

- Round to the nearest tenth

Round 86.67 to the nearest tenth. 86.67 rounds to 86.7

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Key Concepts

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

Fraction to Decimal Conversion
To convert a fraction to a decimal, you need to divide the numerator (the top number) by the denominator (the bottom number). In the given exercise, the fraction is \(\frac{13}{15}\). To convert this to decimal, divide 13 by 15. Applying the division, we get: \(\frac{13}{15} = 0.8667\). This means the fraction \(\frac{13}{15}\) is equivalent to approximately 0.8667 in decimal form. It鈥檚 important to know how to perform this conversion since decimals are often easier to work with in further calculations.
Decimal to Percentage Conversion
Turning a decimal into a percentage is straightforward. You just need to multiply the decimal by 100. This is because 'percent' means 'per hundred.' To put it simply, the decimal is converted to a number out of 100. Looking at the exercise, we have a decimal of 0.8667. To convert this to a percentage, multiply it by 100: \(0.8667 \times 100 = 86.67\). This means 0.8667 as a percentage is 86.67%. So whenever you see a decimal and need to express it as a percentage, remember to multiply it by 100.
Rounding Decimals
Rounding decimals is a common technique to simplify numbers, making them easier to understand and work with. When rounding to the nearest tenth, focus on the digit in the hundredths place (second digit to the right of the decimal point). In our example, we have 86.67. The number in the hundredths place is 7. If this number is 5 or greater, round the tenths place up. If it鈥檚 less than 5, leave the tenths place as is. Here, the 7 means we round 86.67 up to 86.7. This gives us a more manageable number while maintaining accuracy in most situations.

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