Rounding Numbers

Key Vocabulary

Integer: a number that is not a fraction, therefore is a whole number.

Rounding to the nearest whole number

When we count, we use whole numbers like 1, 2, 3, and so on. Sometimes we have numbers with a decimal point, like 2.5 or 3.7. Rounding to the nearest whole means we want to find the closest whole number.

 Example 1

 Let’s say we have the number 2.8

2.8 would sit somewhere on this number line between 2 and 3. Therefore we know that when we are rounding to the nearest whole number the answer will be either 2 or 3

 Let's see where it goes…

Let's see how far away from the 2 and from the 3

We can see that 2.8 is only 0.2 away from 3 whereas it is 0.8 away from 2.

 So we would round 2.8 to 3

 However! It is not always convenient to draw a number line every

 Luckily there is a quicker way!

To round a number to the nearest whole number, we look at the number after the decimal point. If that number is 5 or more, we round up to the next whole number. If it's less than 5, we round down to the previous whole number.

We have a rhyme that can help us remember this:

 5 or more let is soar (round up)

4 or less let it rest (round down)

So, let’s look at the same example and try it with this new technique:

First we need to look at the number after the decimal

We can see that the number after the decimal is an 8

Let’s look at our rhyme again

5 or more let is soar (round up)

4 or less let it rest (round down)

 8 is ‘5 or more let is soar’ so therefore we round it up

Example 2

let's say we have the number 4.3.

We look at the number after the decimal point (which is 3) and see that it's less than 5, so we round down to the previous whole number.

The previous whole number before 4.3 is 4,

so 4.3 rounded to the nearest whole number is 4.

Rounding to the nearest 10^th (Rounding to 1 decimal place)

Sometimes we need to be more specific when we write an answer.. sometimes we need to round to the nearest 10^th (rounding to 1 decimal place)

 To round a number to the nearest 10th, you need to look at the digit in the hundredths place.

If that digit is 5 or greater, you round up the tenths digit. If it is less than 5, you round down the tenths digit.

Example 1 

Let's say you have the number 3.68 and you want to round it to the nearest 10th.

1. Look at the digit in the hundredths place, which is 8.
2. Since 8 is greater than 5, you need to round up the tenths digit, which is 6.
3. So the number rounded to the nearest 10th is 3.7

Example 2 

Let's say you have the number 2.34 and you want to round it to the nearest 10th.

1. Look at the digit in the hundredths place, which is 4.
2. Since 4 is less than 5, you need to round down the tenths digit, which is 3.
3. So the number rounded to the nearest 10th is 2.3

Rounding to the nearest 100^th (2 decimal places)

If we are wanting even more ‘detail’ in our answer we can round to 2 decimal places, or round to the nearest 100^th

To round to the nearest 100th, you need to look at the digit in the thousandth place and determine whether it is closer to the previous hundredth or the next hundredth.

Here are the steps to round to the nearest 100th:

1. Look at the digit in the thousandth place. If it is 5 or greater, round up. If it is less than 5, round down.
2. If you are rounding up, add 1 to the hundredth place. If you are rounding down, leave the hundredth place as it is.
3. If you end up with a result of 100 in the hundredth place, round the integer up to the next whole number and set the hundredth place to 0

Example 1

Let's say you have the number 3.4567 and you want to round it to the nearest 100th.

1. The digit in the thousandth place is 6, which is greater than 5, so you need to round up.
2. Add 1 to the hundredth place, which gives you 3.46.
3. The result is not 100 in the hundredth place, so you're done.

Therefore, the rounded number to the nearest 100th is 3.46