Ordering Fractions, Decimals & Percentages (Cambridge (CIE) IGCSE Maths: Extended): Revision Note

A calculator can be used to quickly convert any quantities into decimals.

E.g. A fraction can be entered as a division.

Without use of a calculator, write these numbers in order, starting with the smallest.

 $\frac{1}{3}$, $\frac{2}{5}$, $\frac{9}{25}$, $\frac{4}{15}$

Answer:

As they are all fractions, write them with a common denominator
The lowest common denominator is 75
Rewrite each fraction with a denominator of 75

 $\frac{1}{3}=\frac{25}{75}$ $\frac{2}{5}=\frac{30}{75}$ $\frac{9}{25}=\frac{27}{75}$ $\frac{4}{15}=\frac{20}{75}$

Compare and write in order from smallest to largest

$\frac{20}{75},\frac{25}{75},\frac{27}{75},\frac{30}{75}$

Rewrite in their original form

$\frac{4}{15},\frac{1}{3},\frac{9}{25},\frac{2}{5}$

Without use of a calculator, write these numbers in the spaces below.

$\frac{7}{8}$, $\frac{5}{6}$, $0.8$, $78\%$

..... < ..... < ..... < ..... 

Answer:

As there is a mixture of fractions, decimals, and percentages, rewrite each as a decimal

0.8 is already a decimal

Convert 78% to a decimal by dividing by 100

$78\%=0.78$

Convert $\frac{7}{8}$ to a decimal by either using short division, or halving three times

$\begin{array}{rcl}7÷2& =& 3.5\\ 3.5÷2& =& 1.75\\ 1.75÷2& =& 0.875\end{array}$
so $\frac{7}{8}=0.875$

Convert $\frac{5}{6}$ to a decimal by using short division

$60.833...5225.000...$

so $\frac{5}{6}=0.8333...=0.8\dot{3}$

Write them all with 3 decimal places to determine the order

$$\begin{gathered} 0.875 \\ 0.833 \\ 0.800 \\ 0.780 \end{gathered}$$

Rewrite the decimals in order

$0.78,0.8,0.8\dot{3},0.875$

Rewrite in their original form, and recall that < means "less than", so the smallest value will be first

$78\%<0.8<\frac{5}{6}<\frac{7}{8}$