Rounding Numbers

Rounding Numbers

Some questions that your child may come across may ask them to round a number to the nearest 10, 100boldsymbol{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 5boldsymbol{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.

  1. Identify the digit you are rounding and look at the digit to the right of it.
  2. If the digit to the right is 5textcolor{red}{5} or above, the number rounds up.
  3. If the digit to the right is less than 5textcolor{red}{5}, the number rounds down.

It is best to get to grips with this topic with some examples.

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Example 1: Rounding to the nearest 10, 100boldsymbol{10,,100} and 1000boldsymbol{1000}

Here are some examples you can work through with your child to help them get to grips with rounding.

a) Round 342textcolor{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 2textcolor{red}{2}.

34234textcolor{red}{2}

This digit is less than 55.

So, 342textcolor{blue}{342} rounds down to 340textcolor{blue}{340}.

b) Round 1552textcolor{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 5textcolor{red}{5}.

155215textcolor{red}{5}2

This digit is 55 or above.

So, 1552textcolor{blue}{1552} rounds up to 1600textcolor{blue}{1600}.

c) Round 9903textcolor{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 9textcolor{red}{9}.

99039textcolor{red}{9}03

This digit is 55 or above.

So, 9903textcolor{blue}{9903} rounds up to 10 000textcolor{blue}{10,000}

This is an interesting example as the digit, 99 seems to round to 00 and then a 11 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 1010 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 1.482textcolor{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 8textcolor{red}{8}.

1.4821.4textcolor{red}{8}2

This digit is a 55 or above.

So, 1.482textcolor{blue}{1.482} rounds up to 1.5textcolor{blue}{1.5}.

b) Round 4.903textcolor{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 3textcolor{red}{3}.

4.9034.90textcolor{red}{3}

This digit less than 55.

So, 4.903textcolor{blue}{4.903} rounds down to 4.90textcolor{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+889342 + 889

A student has got the answer 12311231

To check whether this answer is in the correct area, they can use rounding to estimate the original calculation.

Round 342342 and 889889 to the nearest hundred and then add them together.

The calculation then becomes easier for the student to confidently answer.

300+900=1200300 + 900 = 1200

As we can see 12001200 is pretty close to 12311231 so the student can feel more confident they have the correct answer.

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Rounding Numbers Example Questions

Question 1: Round 56.28 kg56.28 text{ kg} to the nearest 100100 grams.

[2 marks]

First your child will need to convert kilograms into grams so that the units in the question match.

There are 10001000 grams in a kilogram.

56.28 kg×1000=56 280 g56.28text{ kg} times 1000 = 56,280text{ g}

As the units now aren’t relevant, the question becomes:

Round 56 28056,280 to the nearest 100100

The digit to the right of the hundreds column is an 8textcolor{red}{8}.

This digit is 55 or above.

So, we round up and the answer is 56 30056,300 grams.

Question 2: Round 0.8420.842 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.

0.8420.textcolor{red}{8}42

In this case that digit is an 8textcolor{red}{8}.

This digit is 55 or above.

So, 0.842textcolor{blue}{0.842} rounds up to 1textcolor{blue}{1}

Question 3: Robin is answering the following calculation in their maths homework.

Calculate 792×8792 times 8

Robin’s answer is 6336663366

By estimating the calculation, decide whether Robin has got the correct answer.

[2 marks]

The calculation 792×8792 times 8 is tricky but if we round 792792 to the nearest hundred it becomes a lot more manageable for your child.

The digit to the right of the hundreds column is a 9textcolor{red}{9}.

7927textcolor{red}{9}2

This digit is 55 or above.

So, 792textcolor{blue}{792} rounds up to 800textcolor{blue}{800}.

Now Robin’s calculation becomes:

800×8=6400800 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.