Ordering Numbers

All numbers have three digits.

Look at the digits in the hundreds columns.

$textcolor{red}{6}56,,,textcolor{red}{5}55,,,textcolor{red}{5}56,,,textcolor{red}{6}65$

As $textcolor{red}{6}$ is larger than $textcolor{red}{5}$, $656$ and $665$ are larger than $555$ and $556$.

Next, looking at the tens column to find the largest.

$6textcolor{red}{5}6,,,6textcolor{red}{6}5$

So, $665$ is the largest number followed by $656$.

Now comparing the digits in the tens column for the remaining numbers.

$5textcolor{red}{5}5,,,5textcolor{red}{5}6$

Both digits are the same so we move on to compare the digits in the units column.

$55textcolor{red}{5},,,55textcolor{red}{6}$

From this we can deduce the correct answer is:

$555,,,556,,,656,,,665$

These numbers are in the same format of two digits before the decimal point and one digit after the decimal point except for $34$. We can rewrite this as $34.0$ so that it matches up and is easier to compare.

$34.2,,,33.1,,,33.3,,,34.0$

Now we can approach the question as we normally would.

Looking at the tens column first.

$textcolor{red}{3}4.2,,,textcolor{red}{3}3.1,,,textcolor{red}{3}3.3,,,textcolor{red}{3}4.0$

They are all the same digit so we will need to look to the units column.

$3textcolor{red}{4}.2,,,3textcolor{red}{3}.1,,,3textcolor{red}{3}.3,,,3textcolor{red}{4}.0$

From this we can see that $34.2$ and $34.0$ are larger than $33.1$ and $33.3$

Then, we need to look at the tenths column to find the largest number.

$34.textcolor{red}{2},,,34.textcolor{red}{0}$

So, the largest number is $34.2$ followed by $34.0$.

Next compare the digits in the tenths column to find which is the smallest.

$33.textcolor{red}{1},,,33.textcolor{red}{3}$

So, our final order becomes:

$34.2,,,34,,,33.3,,,33.1$

Let’s unpick what the question is asking us to do!

We have a list of prices (which are just decimals) and we want to order them from cheapest to most expensive, so in other words smallest to largest.

First, list the numbers out.

$2.15,,,,2.51,,,3.05,,,2.55$

All of the numbers have the same number of digits before the decimal point and the same number of digits after the decimal point.

Next, look at the units column.

$textcolor{red}{2}.15,,,textcolor{red}{2}.51,,,textcolor{red}{3}.05,,,textcolor{red}{2}.55$

From this we can identify that $3.05$ is the largest (or most expensive).

Then let’s use the tenths column for the rest of our numbers.

$2.textcolor{red}{1}5,,,2.textcolor{red}{5}1,,,2.textcolor{red}{5}5$

This tells us that $2.15$ is the smallest or the cheapest.

We will have to look at the hundredths column to distinguish between the final two prices.

$2.5textcolor{red}{1},,,2.5textcolor{red}{5}$

So, the correct order is:

$pounds 2.15,,, pounds 2.51,,, pounds 2.55,,, pounds 3.05$

Or ordering the items like asked in the question gives us the final answer of…

Cup of tea, Cup of coffee, Lemonade, Milkshake