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 4th decimal place.

75.421652

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

75.421652

 

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.

75.4217

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 6th one.

23.05214

23.05214

23.05214

23.05214

23.05214

23.05214

23.05214

So, the 1 is our 6th significant figure

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

23.05214

 

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.

23.0521

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 6th one.

0.04312

0.04312

0.04312

So, the 3 is the 2nd significant figure

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

0.04312

 

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.

0.043

Example Questions

Question 1: Round 3.2156 to 2 decimal places.

Answer

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

 

We’re rounding to the 2nd decimal place.

 

3.2156

 

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

 

3.2156

 

 

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.

Answer

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 1st one.

 

0.0007689

0.0007689

 So, the 7 is the 1st significant figure

 

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

 

0.0007689

 

 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