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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.
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
Therefore, if we want to express the above number as a percentage, we obtain
Write the following fractions as percentages (in three significant figures).
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
The advantage of expressing fractions as percentages is evident when encountering daily life situations like the one presented below.
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.
The participants in the poll who answered A were 329 out of 1247 people. Therefore, we have
People who answered A = 329/1247
People who answered B = 217/1247
People who answered C = 340/1247
People who answered D = 168/1247
The number of people who didn't respond or were undecided is calculated by subtracting all the above categories from the total. Thus,
Let's find the percentage of participants in the poll these people represent. We have
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
which however is a satisfactory result. Obviously, if the rounding were more accurate (at more decimal places), the result would be closer to 100%.
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