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Chapter 7: Problem 68

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{6}{7}$$

Short Answer

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Step by step solution

01

- Convert Fraction to Decimal

To convert the fraction \(\frac{6}{7}\) to a decimal, divide the numerator (6) by the denominator (7). Use a calculator or long division method to get the decimal form.
02

- Calculate the Decimal

Perform the division \(\frac{6}{7} = 0.857142857...\). So, the fraction \(\frac{6}{7}\) is approximately equal to 0.857142857.
03

- Convert Decimal to Percent

To convert the decimal to a percent, multiply the decimal by 100. So, \(0.857142857 \times 100 = 85.7142857\).
04

- Round to the Nearest Tenth of a Percent

Round the result to the nearest tenth. Here, 85.7142857 rounded to the nearest tenth is 85.7%.

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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 transform a fraction into a decimal, you need to divide the numerator (the number on top) by the denominator (the number on the bottom). For example, with the fraction \(\frac{6}{7}\), you would divide 6 by 7. You can use either a calculator or the long division method. When you carry out this division, you get a repeating decimal, which in this case is approximately 0.857142857. This decimal will help in further calculations.
decimal multiplication
Once you have the decimal equivalent of the fraction, the next step is to convert this decimal into a percentage. To achieve this, you multiply the decimal number by 100. This is done because 'percent' means 'per hundred.' For instance, taking our previous result of 0.857142857, we multiply it by 100 to get 85.7142857. It's important to perform this step accurately to ensure a precise conversion.
rounding decimals
After multiplying the decimal by 100, you may end up with a long number. To simplify your result, you often need to round it. In this exercise, we're instructed to round to the nearest tenth of a percent. To do this, look at the hundredths place (the second digit to the right of the decimal point). If the hundredths place is 5 or higher, round up. If it's less than 5, round down. For 85.7142857, you would round the 1 up due to the 4 next to it, arriving at 85.7.
percentage conversion
By rounding the previous result, you now have the fraction represented as a percentage. This is a common way to express fractions since percentages are often easier to understand and compare. For our example, the fraction \(\frac{6}{7}\) converts to approximately 85.7% once rounded. This process makes dealing with fractions in real-world contexts much simpler, particularly in instances that involve statistics, shopping discounts, and more.

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Most popular questions from this chapter

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