How to Convert Ratios to Percents and Vice Versa

Welcome to this tutorial on converting ratios to percents and vice versa, an important part of our 'Ratios in Percents' section. These conversions are common in various areas of mathematics and real-life scenarios. Let's explore!

What is a Ratio?

A ratio is a way of comparing two or more quantities. The symbol used to denote a ratio is ':'. For example, if there are 5 apples and 7 oranges in a fruit basket, the ratio of apples to oranges is 5:7.

What is a Percent?

A percent, as we learned in our previous tutorial, is a way of expressing a number as a fraction of 100. The symbol for percent is '%'. So, if we say 30%, we mean 30 out of 100.

How to Convert Ratios to Percents

To convert a ratio to a percent, we first express the ratio as a fraction, then convert this fraction to a decimal, and finally multiply the decimal by 100 to get the percentage.

For example, to convert the ratio 3:4 to a percent:
First, we convert the ratio to a fraction: 3/4
Then, we convert the fraction to a decimal: 3 ÷ 4 = 0.75
Finally, we convert the decimal to a percent: 0.75 × 100 = 75%

How to Convert Percents to Ratios

Converting a percent to a ratio involves reversing the above steps. You first divide the percentage by 100 to get a decimal, then convert this decimal to a fraction, and finally express this fraction as a ratio.

For example, to convert 80% to a ratio:
First, we convert the percent to a decimal: 80 ÷ 100 = 0.8
Then, we convert the decimal to a fraction: 0.8 = 4/5
Finally, we convert the fraction to a ratio: 4:5

Practice Converting Between Ratios and Percents

Let's put our new knowledge to the test with some practice exercises. Try converting the following ratios to percentages and vice versa:

Ratios to Percents: 2:5, 7:10, 3:4
Percents to Ratios: 40%, 70%, 75%

Remember, the more you practice, the easier these conversions will become!

Applications of Converting Between Ratios and Percents

Converting between ratios and percentages is a common requirement in various fields, including statistics, finance, engineering, and physics. For example, a change in a quantity can be expressed either as a ratio or a percent, which can be helpful in comparing different quantities or understanding changes over time.

Conclusion

Being able to convert between ratios and percents is an important mathematical skill. We hope this tutorial has made the process clear and straightforward. Stay tuned for more insightful lessons in our 'Ratios in Percents' section!

Ratios in Percents Tutorials

If you found this ratio information useful then you will likely enjoy the other ratio lessons and tutorials in this section:

Next: Ratios and Rates