Question

Write each fraction or decimal as a percent. Round to the nearest tenth of a percent. $$\frac{4}{5}$$

Short answer

80%

Step-by-step solution

Convert Fraction to Decimal

Divide the numerator by the denominator to convert the fraction \(\frac{4}{5}\) into a decimal. \[ \frac{4}{5} = 0.8 \]

Convert Decimal to Percent

Multiply the decimal result obtained from the previous step by 100 to convert it into a percent. \[0.8 \times 100 = 80\%\]

Round to the Nearest Tenth

Check if rounding is necessary. In this case, 80 is already a whole number, thus no rounding is required.

Key concepts

Fractions to Decimals

Converting fractions to decimals is an essential skill in mathematics. It helps you understand and work with numbers more easily. To convert a fraction like \(\frac{4}{5}\), follow these steps:

• **Step 1**: Divide the numerator (top number) by the denominator (bottom number).
• For the fraction \( \frac{4}{5} \), you would divide 4 by 5.

The result is 0.8, so the decimal equivalent of \(\frac{4}{5}\) is 0.8.

This simple division process turns fractions into decimals, making them easier to understand and work with in various mathematical operations.

Decimals to Percents

Once you have a decimal, converting it to a percent is straightforward. You just need to multiply the decimal by 100. For example, let's use the decimal 0.8 that we got from the previous step:
Multiply 0.8 by 100: \[ 0.8 \times 100 = 80 \]

Now, write the result with a percent symbol (%) to indicate that it is a percentage. So, 0.8 is equal to 80%.

• **Step 1**: Take your decimal (0.8).
• **Step 2**: Multiply it by 100.
• **Step 3**: Add the percent symbol to the result.

Thus, 0.8 becomes 80%.

Rounding Percents

Rounding percents is useful when you want to simplify the numbers for easier interpretation. For example, in the exercise, the percent we calculated was exactly 80%. However, rounding is very important when your decimal multiplication does not result in a whole number.
Here’s how to round to the nearest tenth of a percent:

• **Step 1**: Look at the number in the hundredths place (the second digit to the right of the decimal point).
• **Step 2**: If this number is 5 or greater, round the tenths place up by one. Otherwise, leave the tenths place unchanged.

For instance, if you had 80.45%, you'd look at the .45.Since 45 is greater than 5, you'd round up the 80.4 to 80.5%.

In our example, since we had 80%, no rounding was required. But remember, this step is handy when you have more complex decimals.