Rounding Numbers (SQA National 5 Applications of Mathematics): Revision Note

Rounding to decimal places

How do I round a number to a given decimal place?

• STEP 1
  Identify the position of the decimal place you are rounding to

  • e.g. to round 23.5672 to three decimal places find the third decimal place (0.007)

• STEP 2
  Identify the two closest numbers which have the required number of decimal places

  • e.g. 23.5672 is between 23.567 and 23.568

• STEP 3
  Circle the number to the right of the required decimal place

  • If the circled number is 5, 6, 7, 8 or 9 then you round to the bigger number

  • If the circled number is 0, 1, 2, 3 or 4 then you round to the smaller number

    • e.g. rounds to 23.567

Rounding to significant figures

What are significant figures?

• Significant figures of a number are the digits that tell you its value

  • It ignores the zeroes at the start of a number

  • These do not tell you anything about the number

    • e.g. 043 is the same as 43

• The first significant figure is the first non-zero digit (i.e. the non-zero digit with the largest place value)

  • The first significant figure of 3097 is 3

  • The first significant figure of 0.0607 is 6

• All digits after the first significant figure are also significant

  • Even the zeroes

    • 0 is the second significant figure of 3097

    • 9 is the third significant figure of 3097

How do I round a number to a given number of significant figures?

• STEP 1
  Identify the position of the significant figure you are rounding to

  • e.g. the third significant figure of 23.5672 is 5

• STEP 2
  Identify the two closest numbers which have the required number of significant figures

  • e.g. 23.5672 is between 23.5 and 23.6

• STEP 3
  Circle the number to the right of the required decimal place

  • If the circled number is 5, 6, 7, 8 or 9 then you round to the bigger number

  • If the circled number is 0, 1, 2, 3 or 4 then you round to the smaller number

    • e.g. rounds to 23.6

Rounding in context

When do I round my answer?

• You should only round at the end of a question

  • Otherwise, it is possible to get rounding errors

• You can use the ANS button on your calculation to use the full previous answer

• Alternatively, use at least 4 digits in your calculations

How do I know what degree of accuracy to give my answer to?

• The question usually tells you how to round your answer if there is a mark for rounding

• Otherwise, you can normally choose how to round your answer

How do I round my answer with money?

• In money calculations, unless the required degree of accuracy is stated in the question, you can look at the context

  • Round to 2 decimal places

    • e.g. £64.749214 will round to £64.75

  • Or to the nearest whole number, if this seems sensible (for example, other values are whole numbers)

    • £246 029.8567 rounds to £246 030

How do I choose when to round to the next or previous whole number?

• Think carefully about the context

• You usually round to the next whole number when finding a minimum value

  • e.g. find the minimum number of buses needed for 100 students given that each bus can hold 12 students

    • 100 ÷ 12 = 8.33333...

    • However, 8 buses is not enough for all the students

    • Round to the next whole number to get 9 buses

• You usually round to the previous whole number when finding a maximum value

  • e.g. find the maximum number of cakes that can be made with 1700 grams of flour given that each cake needs 300 grams of flour

    • 1700 ÷ 300 = 5.66666...

    • However, there is not enough flour for 6 cakes

    • Round to the previous whole number to get 5 cakes