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.

6\textcolor{red}{5}6,\,\,6\textcolor{red}{6}5

So, 665 is the largest number followed by 656.

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

5\textcolor{red}{5}5,\,\,5\textcolor{red}{5}6

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

55\textcolor{red}{5},\,\,55\textcolor{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.

3\textcolor{red}{4}.2,\,\,3\textcolor{red}{3}.1,\,\,3\textcolor{red}{3}.3,\,\,3\textcolor{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.

2.5\textcolor{red}{1},\,\,2.5\textcolor{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