Rounding Numbers
Rounding Numbers
Some questions that your child may come across may ask them to round a number to the nearest \boldsymbol{\textcolor{darkturquoise}{10,\,100}} or whole number, for example. Your child also may be required to round to a specified number of decimal places which can be a bit trickier.
In this section, we will discuss the number \boldsymbol{\textcolor{darkturquoise}{5}} and why it is important when rounding numbers and how your child can use rounding to check their answers.
Rules of Rounding
When rounding numbers there are a couple of simple rules for your child to become familiar with that will make this topic easier.
- Identify the digit you are rounding and look at the digit to the right of it.
- If the digit to the right is \textcolor{red}{5} or above, the number rounds up.
- If the digit to the right is less than \textcolor{red}{5}, the number rounds down.
It is best to get to grips with this topic with some examples.
Example 1: Rounding to the nearest \boldsymbol{10,\,100} and \boldsymbol{1000}
Here are some examples you can work through with your child to help them get to grips with rounding.
a) Round \textcolor{blue}{342} to the nearest ten.
We are rounding to the nearest ten therefore we want to look at the digit to the right of the tens column.
In this case that digit is a \textcolor{red}{2}.
34\textcolor{red}{2}
This digit is less than 5.
So, \textcolor{blue}{342} rounds down to \textcolor{blue}{340}.
b) Round \textcolor{blue}{1552} to the nearest hundred.
This time we are rounding to the nearest hundred so the digit we are interested in is the one to the right of the hundreds column.
In this case that digit is a \textcolor{red}{5}.
15\textcolor{red}{5}2
This digit is 5 or above.
So, \textcolor{blue}{1552} rounds up to \textcolor{blue}{1600}.
c) Round \textcolor{blue}{9903} to the nearest thousand.
We are rounding to the nearest thousand so the digit to the right is found in the hundreds column.
In this case that digit is a \textcolor{red}{9}.
9\textcolor{red}{9}03
This digit is 5 or above.
So, \textcolor{blue}{9903} rounds up to \textcolor{blue}{10\,000}
This is an interesting example as the digit, 9 seems to round to 0 and then a 1 is added onto the column to the left of it. A good way for your child to think about this is that we are rounding up to 10 but can’t fit both digits into one column.
Example 2: Rounding to Decimal Places
Your child may also be asked to round to decimal places. This works in the same way as we have seen before, here are some examples to help familiarise your child with rounding to decimal places.
a) Round \textcolor{blue}{1.482} to one decimal place or to the nearest tenth.
The first decimal place is the digit directly to the right of the decimal point. So, if we are rounding to one decimal place we need to look at the digit to the right of the first decimal place.
In this case that digit is an \textcolor{red}{8}.
1.4\textcolor{red}{8}2
This digit is a 5 or above.
So, \textcolor{blue}{1.482} rounds up to \textcolor{blue}{1.5}.
b) Round \textcolor{blue}{4.903} to two decimal places or to the nearest hundredth.
The digit to the right of the second decimal place is the third decimal place.
In this case that digit is a \textcolor{red}{3}.
4.90\textcolor{red}{3}
This digit less than 5.
So, \textcolor{blue}{4.903} rounds down to \textcolor{blue}{4.90}.
Estimating Answers
When your child is faced with a question that they’ve answered but are unsure about, rounding can help them to estimate the answer and hence feel more confident that the answer they have written is correct.
Example: Calculate 342 + 889
A student has got the answer 1231
To check whether this answer is in the correct area, they can use rounding to estimate the original calculation.
Round 342 and 889 to the nearest hundred and then add them together.
The calculation then becomes easier for the student to confidently answer.
300 + 900 = 1200
As we can see 1200 is pretty close to 1231 so the student can feel more confident they have the correct answer.
Rounding Numbers Example Questions
Question 1: Round 56.28 \text{ kg} to the nearest 100 grams.
[2 marks]
First your child will need to convert kilograms into grams so that the units in the question match.
There are 1000 grams in a kilogram.
56.28\text{ kg} \times 1000 = 56\,280\text{ g}
As the units now aren’t relevant, the question becomes:
Round 56\,280 to the nearest 100
The digit to the right of the hundreds column is an \textcolor{red}{8}.
This digit is 5 or above.
So, we round up and the answer is 56\,300 grams.
Question 2: Round 0.842 to the nearest whole number.
[1 mark]
The nearest whole number is the same as saying the nearest unit so the digit we are interested in is the digit to the right of the units column.
0.\textcolor{red}{8}42
In this case that digit is an \textcolor{red}{8}.
This digit is 5 or above.
So, \textcolor{blue}{0.842} rounds up to \textcolor{blue}{1}
Question 3: Robin is answering the following calculation in their maths homework.
Calculate 792 \times 8
Robin’s answer is 63366
By estimating the calculation, decide whether Robin has got the correct answer.
[2 marks]
The calculation 792 \times 8 is tricky but if we round 792 to the nearest hundred it becomes a lot more manageable for your child.
The digit to the right of the hundreds column is a \textcolor{red}{9}.
7\textcolor{red}{9}2
This digit is 5 or above.
So, \textcolor{blue}{792} rounds up to \textcolor{blue}{800}.
Now Robin’s calculation becomes:
800 \times 8 = 6400
So, we can see that Robin must have gone wrong somewhere in their working out and should have another look at the question.