Ordering and comparing numbers Worked Solutions — GCSE Maths

Spot the negative numbers

Negative numbers are always smaller than 0 and any positive number. On a number line they sit to the left of zero.

Order the negatives

For negatives, the bigger the digit the smaller the number. Think of $-8^{\circ}$C being colder than $-3^{\circ}$C.

Write the full ascending list

Place the negatives first, then 0, then the positives in normal order. This is smallest to largest.

Picture a number line

On a number line $-6$ is further to the left than $-2$. Numbers get smaller as you move left.

Compare the two negatives

Being further left means $-6$ is the smaller number. It is lower/colder than $-2$.

Choose the symbol

The pointed end of $<$ points at the smaller number. So we write $-6 < -2$.

Give each the same number of decimal places

Adding zeros on the end does not change the value but lines up the columns. Remember $0.5 = 0.500$.

Compare digit by digit

Start in the tenths column, then hundredths, then thousandths. The first column where they differ decides the order.

Write back in original form

Put the original decimals into that order. That is the ascending list.

Match the decimal places

Write $0.7$ as $0.70$ so both have two decimal places. Now it is a fair comparison.

Compare as hundredths

$0.70$ is 70 hundredths and $0.68$ is 68 hundredths, so $0.70$ is bigger.

Choose the symbol

So $0.7$ is greater. A common mistake is thinking $0.68$ is bigger just because it has more digits.

Find the temperatures below zero

Temperatures below $0^{\circ}$C are the coldest. Here $-5$ and $-1$ are below zero.

Order the negatives, coldest first

$-5^{\circ}$C is colder than $-1^{\circ}$C because it is further below zero.

Complete the list to warmest

Then comes $0$, then the positive temperatures in order. That runs coldest to warmest.