Unit 4 Section 5 : Rounding

We round numbers if we only need a reasonable approximation rather than the exact value.

Rounding a number can be done:
- to a certain number of decimal places
- to a certain number of significant figures
- to the nearest whole number (or to the nearest ten, hundred, thousand etc.)

All rounding follows the same basic steps:

  1. Decide where you want to cut off the number, and mark a "cut-off point".
  2. If the digit after the cut-off point is 5 or more, then increase the digit before the cut-off point by one.
  3. Remove all the digits after the cut-off point (but not a decimal point if there is one).
  4. If there are any gaps between the cut-off point and the decimal point, fill them with zeroes.

 

Rounding to N decimal places

To do this, place the cut-off point after the Nth decimal place, then carry out the above steps.

Example
Round these numbers to the specificed number of decimal places:
(a) 6.2348 to 2 decimal places
(1) First we place the cut-off point after the 2nd decimal place: 6 . 2 3|4 8
(2) The digit after the cut-off point is not 5 or more, so the digit before it is not changed: 6 . 2 3|4 8
(3) The digits after the cut-off point are removed: 6 . 2 3|
(4) There are no gaps to fill between the cut-off point and the decimal point, so our answer is: 6 . 2 3 (2 d.p.)
(b) 5.2718 to 3 decimal places
(1) First we place the cut-off point after the 3rd decimal place: 5 . 2 7 1|8
(2) The digit after the cut-off point is 5 or more, so the digit before it is increased by 1: 5 . 2 7 2|8
(3) The digits after the cut-off point are removed: 5 . 2 7 2|
(4) There are no gaps to fill between the cut-off point and the decimal point, so our answer is: 5 . 2 7 2 (3 d.p.)

Practice Questions
Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.
(a) Round 13.68952 to 1 decimal places

(b) Round 13.68952 to 3 decimal places

(c) Round 13.68952 to 4 decimal places

 

Rounding to N significant figures

To do this, place the cut-off point after the Nth significant figure, then carry out the above steps.
The first significant figure in a number is the first non-zero digit (reading from left to right).
The remaining digits to the right are all significant figures.

The diagram below shows the significant figures in the numbers 302.150 and 0.005106

Example
Round these numbers to the specificed number of significant figures:
(a) 523.591 to 4 significant figures
(1) First we place the cut-off point after the 4th significant figure: 5 2 3 . 5|9 1
(2) The digit after the cut-off point is 5 or more, so the digit before it is increased by 1: 5 2 3 . 6|9 1
(3) The digits after the cut-off point are removed: 5 2 3 . 6|
(4) There are no gaps to fill between the cut-off point and the decimal point, so our answer is: 5 2 3 . 6 (4 s.f.)
(b) 3441.5 to 2 significant figures
(1) First we place the cut-off point after the 2nd significant figure: 3 4|4 1 . 5
(2) The digit after the cut-off point is not 5 or more, so the digit before it is unchanged: 3 4|4 1 . 5
(3) The digits after the cut-off point are removed (but not the decimal point): 3 4|_ _ . _
(4) The gaps between the cut-off point and the decimal point are filled with zeroes, giving: 3 4 0 0 (2 s.f.)

Practice Questions
Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.
(a) Round 3.642 to 2 significant figures

(b) Round 314769 to 3 significant figures

(c) Round 0.00723 to 1 significant figures

 

Rounding to the nearest 1, 10, 100, 1000 etc.

To do this, place the cut-off point after the relevant place value. For example, if you want to
round to the nearest 100 then you need to place the cut-off point after the "hundreds" column.

The diagram below shows the place values in the number 4892.1

Example
Round the number 4892.1 to the specificed accuracy:
(a) to the nearest 10
(1) First we place the cut-off point after the tens column: 4 8 9|2 . 1
(2) The digit after the cut-off point is not 5 or more, so the digit before it is unchanged: 4 8 9|2 . 1
(3) The digits after the cut-off point are removed: 4 8 9|_ . _
(4) The gaps between the cut-off point and the decimal point are filled with zeroes, giving: 4 8 9 0 (nearest 10)
(b) to the nearest thousand
(1) First we place the cut-off point after the thousands column: 4|8 9 2 . 1
(2) The digit after the cut-off point is 5 or more, so the digit before it is increased by 1: 5|8 9 2 . 1
(3) The digits after the cut-off point are removed (but not the decimal point): 5|_ _ _ . _
(4) The gaps between the cut-off point and the decimal point are filled with zeroes, giving: 5 0 0 0 (2 s.f.)

Practice Questions
Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.
(a) Round 3647.5 to the nearest 10

(b) Round 3647.5 to the nearest 100

(c) Round 3647.5 to the nearest 1000

(d) Round 3647.5 to the nearest 1 (whole number)

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

Question 1
Round each of the numbers below to the nearest 1 (whole number):
(a) 4.3
(b) 2.04
(c) 16.9
(d) 3.5
(e) 33.49
(f) 18.65
Question 2
Round each of the numbers below to the nearest 10
(a) 187
(b) 309
(c) 8
(d) 35
(e) 44.9
(f) 16.4
Question 3
The attendance at a football match was 36475 people.
Round this number to:
(a) the nearest 1000
(b) the nearest 100
(c) the nearest 10
Question 4
Write each of these numbers correct to 2 decimal places:
(a) 4.263
(b) 0.0472
(c) 10.8374
(d) 82.062
(e) 3.445
(f) 9.395
Question 5
Write each of these numbers correct to 2 significant figures:
(a) 1.473
(b) 6.254
(c) 3.216
(d) 10.68
(e) 142
(f) 1374
Question 6
Write the number 8.645712 correct to:
(a) 3 decimal places
(b) 4 decimal places
(c) 1 decimal place
Question 7
Write the number 147.52 correct to:
(a) 4 significant figures
(b) 3 significant figures
(c) 2 significant figures
(d) 1 significant figure
Question 8
Write the number 104.735 correct to:
(a) the nearest 1 (whole number)
(b) 2 decimal places
(c) 2 significant figures
(d) 1 decimal place
(e) 1 significant figure
Question 9
Write each of these numbers correct to 3 significant figures:
(a) 18.47
(b) 0.003265
(c) 147300
(d) 62.999
(e) 0.036247
(f) 0.00036945

You have now completed Unit 4 Section 5
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