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Chapter 7: Problem 70

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{3}{13}$$

Short Answer

Expert verified
23.1%

Step by step solution

01

Convert the Fraction to a Decimal

To convert the fraction \(\frac{3}{13}\) to a decimal, divide the numerator (3) by the denominator (13). \(\frac{3}{13} = 0.23076923077\).
02

Convert the Decimal to a Percent

Multiply the decimal by 100 to convert it to a percentage. \((0.23076923077) \times 100 = 23.076923077\).
03

Round to the Nearest Tenth of a Percent

Round 23.076923077 to the nearest tenth. Look at the hundredths place, which is 7, so round up. This gives us 23.1%.

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Key Concepts

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

Percent Notation
Percent notation is a common way to express a number as a fraction of 100. It uses the percent symbol (%) to show that the number is a part of a whole divided into 100 equal parts.
For example, 50% means 50 out of every 100, or half.
When we convert a fraction to percent notation, it makes it easier to understand and compare with other percentages.
Here's how it's done with our fraction \(\frac{3}{13}\):
  • First, convert the fraction to a decimal.
  • Then, multiply the decimal by 100.
  • Finally, round to the nearest tenth of a percent.
This process ensures we get a precise percentage that represents the fraction accurately.
Fraction to Decimal
Converting a fraction to a decimal involves division. We divide the numerator (top number) by the denominator (bottom number).
In our example, we have \(\frac{3}{13}\):
\(\frac{3}{13} = 0.23076923077\)
This long decimal can be tricky to work with, so typically, we only use the first few digits.
  • Step-by-step, divide 3 by 13.
  • Use a calculator for precision. Simply type in \(.23076923077\).
Rounding Decimals
Rounding decimals is a key mathematical skill. It helps in simplifying numbers and making them easier to understand. Here's how you round a decimal to the nearest tenth:
  • Identify the digit in the tenths place and the digit in the hundredths place.
  • If the hundredths place is 5 or more, round up the tenths place by 1. Otherwise, keep the tenths place the same.
Let's apply this to our example:
We had 23.076923077 after converting to a percent.
Look at the hundredths place, which is 7.
Since 7 is greater than 5, we round the tenths place (which is 0) up by 1.
Therefore, 23.076923077 becomes 23.1% when rounded to the nearest tenth.

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Most popular questions from this chapter

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