**Round Decimal Numbers** *KS3 Revision*

## What you need to know

**Things to remember:**

- When rounding to a given place value, we look at the number to it’s right to see how we round, this is the same for decimals.

– If the number on the right is 5 or more, the place value we’re rounding to goes up by 1.

– If the number on the right is 4 or less, the place value we’re rounding to stays the same.

- Significant figures refers to how many digits there are in a number, starting from the first none zero digit.

Let’s remind ourselves how we round to the nearest 10.

We find the tens and then look to the right.

- If the units are 4 or justify, the tens stay the same and the units become 0.
- If the units are 5 or more, then tens go up by 1 and the units become 0.

Number Rounded

22 20

31 30

65 70

38 49

*Round 75.421652 to 4 decimal places.*

* *

We’ll do this in three steps.

**Step 1: **Find the place value we’re rounding to.

We’re rounding to the 4^{th} decimal place.

75.421**6**52

**Step 2: **Look at the number to the right of the one we’re rounding.

75.421**6**__5__2

* *

**Step 3: **Round the number highlighted in **Step 1 **based on the number in **Step 2**.

The number in **Step 2** was a 5, so the number we’re rounding goes up by 1.

75.421**7**

*Round 23.05214 to 6 significant figures.*

* *

We count significant figures going from left to right, starting with the first non-zero number.

**Step 1: **Find the place value we’re rounding to.

We’re rounding to 6 significant figures, so we need to find the 6^{th} one.

*23.05214*

*2**3.05214*

*2 3.05214*

*23. 05214*

*23.0 5214*

*23.05 214*

*23.052 14*

So, the 1 is our 6^{th} significant figure

**Step 2: **Look at the number to the right of the one we’re rounding.

*23.052 14*

* *

**Step 3: **Round the number highlighted in **Step 1 **based on the number in **Step 2**.

The number in **Step 2** was a 4, so the number we’re rounding doesn’t change.

*23.052 1*

With significant figures, we just need to be careful with decimals, and not including the 0s at the start.

*Round 0.04312 to 2 significant figures.*

* *

We count significant figures going from left to right, starting with the first non-zero number.

**Step 1: **Find the place value we’re rounding to.

We’re rounding to 2 significant figures, so we need to find the 6^{th} one.

*0.04312*

*0.0 4312*

*0.04 312*

So, the 3 is the 2^{nd} significant figure

**Step 2: **Look at the number to the right of the one we’re rounding.

*0.04 312*

* *

**Step 3: **Round the number highlighted in **Step 1 **based on the number in **Step 2**.

The number in **Step 2** was a 1, so the number we’re rounding doesn’t change.

*0.04 3*

## Example Questions

**Question 1:** Round 3.2156 to 2 decimal places.

**Step 1: **Find the place value we’re rounding to.

We’re rounding to the 2nd decimal place.

3.2**1**56

**Step 2: **Look at the number to the right of the one we’re rounding.

3.2**1**56

** **

**Step 3: **Round the number highlighted in **Step 1 **based on the number in **Step 2**.

The number in **Step 2** was a 5, so the number we’re rounding goes up by 1.

3.22

**Question 2:** Round 0.0007689 to 1 significant figure.

We count significant figures going from left to right, starting with the first non-zero number.

**Step 1: **Find the place value we’re rounding to.

We’re rounding to 1 significant figure, so we need to find the 1^{st} one.

0.0007689

0.000**7**689

** **So, the 7 is the 1^{st} significant figure

**Step 2: **Look at the number to the right of the one we’re rounding.

0.000**7**__6__89

** ****Step 3: **Round the number highlighted in **Step 1 **based on the number in **Step 2**.

The number in **Step 2** was a 6, so the number we’re rounding goes up by 1.

0.0008