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Chapter 7: Problem 69

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{1}{13}$$

Short Answer

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Step by step solution

01

Convert the fraction to a decimal

Divide the numerator by the denominator to convert the fraction to a decimal. For the fraction \( \frac{1}{13} \), perform the division: \( 1 \div 13 = 0.076923076923 \).
02

Convert the decimal to a percentage

To convert the decimal to a percentage, multiply by 100: \( 0.076923076923 \times 100 = 7.6923076923 \).
03

Round to the nearest tenth

Round the percentage to the nearest tenth. Look at the digit in the hundredths place (9 in this case). Since it is 5 or greater, round up. Therefore, 7.6923076923 rounded to the nearest tenth is 7.7.

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Key Concepts

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

Decimal Conversion
When you need to convert a fraction into a decimal, you simply divide the numerator by the denominator. Let's take the fraction \(\frac{1}{13}\) as an example. The numerator here is 1, and the denominator is 13. To convert this to a decimal, you perform the division: \(\frac{1}{13} = 0.076923076923\).

This series of numbers may look a bit long, but don't worry. Understanding how to carry out this division is the key, and it involves basic division skills you can easily practice. Once you get the decimal result, you can use it for further calculations.
Percentage Calculation
Converting decimals to percentages is straightforward. You just multiply the decimal by 100. For instance, take the decimal we found in the previous step: \(0.076923076923\). To turn this into a percentage, multiply it by 100.

Here's the math: \(0.076923076923 \times 100 = 7.6923076923\).

So, \(0.076923076923\) becomes roughly 7.6923076923% when multiplied by 100. Remember, multiplying by 100 shifts the decimal place two spots to the right.

Percentages make it easier to understand fractions and decimals in a more intuitive way. This is because percentages are often more relatable in everyday contexts, like discounts and interest rates.
Rounding Numbers
In many cases, you might need to round numbers for simplicity. Rounding to the nearest tenth means looking at the digit in the hundredths place. If this digit is 5 or more, you round up the digit in the tenths place. If it isn't, you round down.

Let's take our percentage, 7.6923076923%. The digit in the hundredths place is 9. Since 9 is greater than 5, you round the tenths digit up.

So, 7.6923076923% rounds to 7.7%.

Rounding off can be very helpful especially in making large numbers more digestible or when making quick estimates. Knowing how to round correctly ensures the accuracy of your simplified numbers.

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Most popular questions from this chapter

Match the percent with its fraction form. a. \(\frac{3}{2}\) b. \(\frac{3}{4}\) c. \(\frac{2}{3}\) d. \(\frac{1}{10}\) e. \(\frac{9}{10}\) f. \(\frac{1}{4}\). $$25 \%$$

Which of the numbers represent \(60 \% ?\) a. 6.0 b. \(0.60 \%\) c. 0.6 d. \(\frac{3}{5}\)

Solve the problem using a percent equation. \(23 \%\) of what number is \(34.5 ?\)

Carson had 600 dollar and spent \(44 \%\) of it on clothes. Then he spent \(20 \%\) of the remaining money on dinner. How much did he spend altogether?

Convert the decimal to a percent. $$0.124$$
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