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Question Video: Comparing Fractions by Converting Them to Recurring Decimals Mathematics

Emma can dig 134/99 holes in an hour, and Charlotte can dig 1 5/18 holes in an hour. By converting both fractions to decimals, determine who is faster at digging holes.

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Video Transcript

Emma can dig 134 over 99 holes in an hour, and Charlotte can dig one and five eighteenths holes in an hour. By converting both fractions to decimals, determine who is faster at digging holes.

In this question, we want to determine which of 134 over 99 and one and five eighteenths is larger by comparing their decimal expansions. First, we input 134 over 99 into the calculator either by typing 134 divided by 99 and pressing the equals button or by using the fraction button as shown, then typing in the numerator and denominator and pressing the equals button. In either case, we can then press the convert from standard form to decimal button, SD, to get the following: 1.353535 and so on. This is a repeated expansion of three five, and we can therefore write this as a recurring decimal. 134 over 99 is equal to 1.35 recurring, where the repeating digits are denoted by either a dot or bar above them.

We can now follow a similar process to write the mixed number one and five eighteenths as a decimal. Using the mixed number button on the calculator, we can input one and five eighteenths. We then press the equals button and finally the conversion button. This gives us the following output on the calculator display: 1.2777 and so on. This time we note that only the digit seven is repeating, so place a dot above this number. One and five eighteenths is equal to 1.27 recurring. Whilst it is not relevant for this question, it is worth noting that this is not the same as 1.27 with dots above both digits after the decimal point, as this would correspond to 1.272727 and so on.

We can see that 1.35 recurring is greater than 1.27 recurring. And we can therefore conclude that Emma is faster at digging holes.

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