### 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.