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Math Lesson 5.2.3 - Converting Non-Decimal Fractions into Percentages

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Welcome to our Math lesson on Converting Non-Decimal Fractions into Percentages, this is the third lesson of our suite of math lessons covering the topic of Percentages, Fractions and Decimals, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Converting Non-Decimal Fractions into Percentages

As we explained in tutorial 3.5, not all fractions can be turned into decimal ones. For example, 2/3 cannot become a decimal fraction as 10 ÷ 3 = 3.333; 100 ÷ 3 = 33.333; etc. Therefore, in many cases it is impossible to find an exact value when converting a non-decimal fraction into decimal, so we use the approximations, which allow us to stop at the desired number of decimal places.

Thus, if we consider the fraction 5/9, the corresponding division is 5 ÷ 9, which gives the value 0.555, which is a recurring decimal. Hence, it is up to the individual when he/she wants to stop by applying known rounding practices. It is very common that in these cases that the question clearly states the answer must be to a specific amount of significant figures, which are the meaningful digits in the value. A number of three significant figures usually corresponds to one decimal place in percentages that are between 10% and 100%, two decimal places for percentages that are between 1% and 10%, three decimal places for percentages below 1% and no decimal places for percentages that are higher than 100%. In this way, we obtain

5/9 ≈ 0.556

Therefore, if we want to express the above number as a percentage, we obtain

5/9 ≈ 55.6%

Example 2

Write the following fractions as percentages (in three significant figures).

  1. 2/7
  2. 13/9
  3. 3/43
  4. 1/402

Solution 2

First we write all fractions as decimals by rounding them to three significant figures, then we express the decimals obtained as fractions. Giving that all the fractions represent recurring decimals, they have the same group of digits (called period) that repeats periodically. Therefore, in all examples we will stop after the first period (before the rounding process takes place) unless the period has more than one digit. Thus, we have

  1. 2/7 = 2 ÷ 7
    = 0.285714
    ≈ 0.286
    = 286/1000
    = 28.6/100
    = 28.6%
  2. 13/9 = 13 ÷ 9
    = 1.444
    ≈ 1.44
    = 144/100
    = 144%
  3. 3/43 = 0.069767441860465116279
    ≈ 0.0698
    = 698/10,000
    = 6.98/100
    = 6.98%
  4. 1/402 = 0.002487562189
    ≈ 0.00249
    = 249/100,000
    = 0.249/100
    = 0.249%

The advantage of expressing fractions as percentages is evident when encountering daily life situations like the one presented below.

Example 3

1247 people participated in a poll where, out of four possible answers (A, B, C and D), 329 people chose A as answer, 217 chose B, 340 chose C, 168 chose D and the rest were undecided or refused to respond. Calculate the corresponding percentages for each category. Express the answers to three significant figures.

Solution 3

The participants in the poll who answered A were 329 out of 1247 people. Therefore, we have

People who answered A = 329/1247

= 329 ÷ 1247
= 0.2638332
≈ 0.264
= 264/1000
= 26.4/100
= 26.4%

People who answered B = 217/1247

= 217 ÷ 1247
= 0.17401764
≈ 0.174
= 174/1000
= 17.4/100
= 17.4%

People who answered C = 340/1247

= 340 ÷ 1247
= 0.27265437
≈ 0.273
= 273/1000
= 27.3/100
= 27.3%

People who answered D = 168/1247

= 168 ÷ 1247
= 0.1347233
≈ 0.135
= 135/1000
= 13.5/100
= 13.5%

The number of people who didn't respond or were undecided is calculated by subtracting all the above categories from the total. Thus,

Unresponsive people = 1247 - 329 - 217 - 340 - 168
= 193 people

Let's find the percentage of participants in the poll these people represent. We have

Unresponsive people = 193/1247
= 193 ÷ 1247
= 0.15477145
≈ 0.155
= 155/1000
= 15.5/100
= 15.5%

These results are not far from the truth; any deflection is due to rounding. Thus, adding all the above percentages (which normally must equal 100%) yields

26.4% + 17.4% + 27.3% + 13.5% + 15.5% = 100.1%

which however is a satisfactory result. Obviously, if the rounding were more accurate (at more decimal places), the result would be closer to 100%.

More Percentages, Fractions and Decimals Lessons and Learning Resources

Percentages Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
5.2Percentages, Fractions and Decimals
Lesson IDMath Lesson TitleLessonVideo
Lesson
5.2.1Converting Decimal Fractions into Percentages
5.2.2Converting Decimals into Percentages
5.2.3Converting Non-Decimal Fractions into Percentages
5.2.4Converting Percentages into Fractions and Decimals
5.2.5Comparing Percentages, Fractions and Decimals

Whats next?

Enjoy the "Converting Non-Decimal Fractions into Percentages" math lesson? People who liked the "Percentages, Fractions and Decimals lesson found the following resources useful:

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  5. Percentages Practice Questions: Percentages, Fractions and Decimals. Test and improve your knowledge of Percentages, Fractions and Decimals with example questins and answers
  6. Check your calculations for Percentages questions with our excellent Percentages calculators which contain full equations and calculations clearly displayed line by line. See the Percentages Calculators by iCalculator™ below.
  7. Continuing learning percentages - read our next math tutorial: Percentage Increase and Decrease

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