Rounding Numbers Worksheets | Questions and Revision | MME

Rounding Numbers Worksheets, Questions and Revision

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What you need to know

Rounding Numbers

Rounding is a process of simplifying a number without changing the value of it too much. We do this by taking a number and working out which of the “simpler” numbers it is closest too. Being confident with decimals is a good idea for this topic. 

Rounding is one of those topics that can come up at any point during the exam. You are unlikely to get a question based only on rounding but multiple questions from different topic areas may ask you to round your answer and this will always be worth a mark .

Another thing to note, is that if you round numbers too early, i.e. during a calculation, then the answer you get at the end may be incorrect, so the general rule is that you only round at the end of an answer, and not during a calculation, unless the question specifically asks you to. 

Rounding

Rounding numbers works as follows:

  • Firstly, determine which digit is your cut-off point, e.g. when rounding 6.2 to the nearest whole number, our cut-off point was the 6.
  • Look at the next digit along after the cut-off point, and determine if it is below 5, or if it is equal to or above 5.
    • If it is below 5, then we round down.
    • If it is 5 or above, then we round up.
  • Finally, all the numbers after the cut-off point become zeros.

There are 3 ways that you might be asked to round a number:

  • To a whole number – the nearest whole number, the nearest 10, the nearest 100,
  • To a given number of decimal places – rounding decimals (often shortened to dp).
  • To a given number of significant figures – rounding significant figures (often shortened to sf).

The way that we outlined rounding above applies to all 3 of these cases, all that differs between them is how you go about choosing the cut-off point. 

Example 1: Rounding to the Nearest 10

Round 235 to the nearest ten.

The first digit, 2, is in hundreds, but the second digit, 3, is in tens, so that will be our cut-off point. Now we look to the digit after this point: it is a 5, which means that we round up, i.e. the cut-off point digit gets increased by 1, so in this case the 3 will become a 4. Finally, making all the digits after the cut-off point zero, we get that

235\,\,\text{ rounded to the nearest 10 is }\,\,240.

Example 2: Rounding Decimals

Round 13.746 to

a) 2 decimal places

b) 1 decimal place.

If we’re rounding to 2 decimal places then the cut-off point is the 2nd decimal place, i.e. the 2nd number after the decimal point. In this case, that is the 4. The digit after the 4 is a 6, which means that we round up and increase the digit before it by 1 so the 4 becomes a 5, giving us

13.746\,\,\text{ rounded to 2 decimal places is }\,\,13.75.

Now, we are rounding 13.746 to 1 decimal place, so our cut-off point is the 1st digit after the decimal point: 7. The digit after the 7 is a 4, which means that we round down and the 7 stays the same, giving us

13.746\,\,\text{ round to 1 decimal place is }\,\,13.7

Example 3: Rounding Decimals

Round 4.398 to 2 decimal places.

The 2nd digit after the decimal point, the 9, is our cut-off point. The digit after it is an 8, so we must round up. The problem is, increasing a 9 by 1 makes 10, so what do we do? The cut-off digit becomes zero, and the digit before it gets increased by 1. So, in this case, the 9 goes to zero and the 3 before it becomes 4. Then, making all the digits after the cut-off point zero, we get

4.398\,\,\text{ rounded to 2 decimal places is }\,\,4.4

Example 4: Rounding Significant Figures

Round 8,529 to 2 significant figures.

We move along our number until we hit a digit that isn’t zero – this is our 1st significant figure. Then, the digit after is the 2nd significant figure, the digit after that is the 3rd, and so on. If any of the digits after the 1st significant figure are zero, they still count as significant figures, it’s only the first one that must be non-zero.

So, in this case, the first digit of the number is an 8 so we start counting right away: 8 is the first significant figure, so 5 is the second significant figure, therefore the 5 is our cut-off point. The digit after the 5 is a 2. This is less than 5, so we round down and the cut-off digit stays the same. Then, making all the digits after the cut-off zero, we get

8,529\,\,\text{ rounded to 2 significant figures is }\,\,8,500.

Example 5: Rounding Significant Figures

Round 0.00589 to 2 significant figures.

So, we need to find the first non-zero term. We can see that the first 3 digits are zero, but the 4th digit is a 5, so this is our 1st significant figure. Therefore, the next digit along, the 8, is our 2nd significant figure and thus is our cut-off point. The digit after the 8 is a 9, which is bigger than 5, and so we round up, increasing the cut-off digit by 1, making the 8 into a 9. Then, making all the digits after the cut-off zero, we get

0.00589\,\,\text{ rounded to 2 significant figures is }\,\,0.0059.

Example Questions

Here we are rounding to the nearest thousand so it is 4th digit we are interested in, 

 

560,180

 

To round up or down we have to consider the value of the digit to its immediate right which in this case is 1.

As 1 is less than 5, we round down and so the zero stays the same and we make the rest of the digits zero,

 

560,180\,\,\text{ rounded to the nearest thousand is }\,\,560,000

Here we are rounding to 1 decimal place so it is the 1st digit after the decimal point we are interested in,

 

97.96

 

To round up or down we have to consider the value of the digit to its immediate right which in this case is 6.

As 6 is greater than 5, we round up. However, as we are rounding up 9 to 10, we have to carry the 1 over to the units column, so we get, 

 

97.96\,\,\text{ rounded to 1 decimal place is }\,\,98.0

Here we are rounding to 3 significant figures so it is the first non-zero digit and the two digits that follow it that we are interested in, 

 

0.02345

 

The 1st significant figure in this case is 2 and moving two places along we see that the 4 is the 3rd significant figure. To round up or down we have to consider the value of the digit to its immediate right which in this case is 5, so we round up, 

 

0.02345\,\,\text{ rounded to 3 significant figures is }\,\,0.0235

Here we are rounding to 3 significant figures so it is the first non-zero digit and the two digits that follow it that we are interested in, 

 

1.0093

 

The 1st significant figure in this case is 1 and moving two places along we see that the 0 is the 3rd significant figure. To round up or down we have to consider the value of the digit to its immediate right which in this case is 9, so we round up, 

 

1.0093\,\,\text{ rounded to 3 significant figures is }\,\,1.01

Here we are rounding to 2 decimal places so it is the 2nd digit after the decimal point we are interested in,

 

55.099

 

To round up or down we have to consider the value of the digit to its immediate right which in this case is 9. As 9 is greater than 5, we round up. However, as we are rounding up 9 to 10, we have to carry the 1 over to the units column, so we get, 

 

55.099\,\,\text{ rounded to 2 decimal places is }\,\,55.10

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