Rounding-And-Estimation Aqa Higher

Rounding & estimation

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

• Identify the digit in the required place value

• Circle the number to the right of the required place value

  • If the circled number is 5 or more then you round to the bigger number

  • If the circled number is less than 5 then you round to the smaller number

  • Put a zero in any following place values before the decimal point

    • E.g. 1567.45 to the nearest 100 would be 1600

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

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

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

  • If the circled number is 5 or more then you round to the bigger number

  • If the circled number is less than 5 then you round to the smaller number

    • E.g. 2.435123 to the nearest 2 d.p. would be 2.44

• When rounding to decimal places make sure you leave your answer with the required amount of decimal places

  • Do not put any zeros after the position of the decimal place you are rounding to

    • E.g. 1267 to the nearest 100 is 1300

    • But 1.267 to two decimal places (nearest 100th) is 1.27 not 1.270

  • If asked for a certain number of decimal places, you must give an answer with that number of decimal places

    • E.g. 2.395 to two decimal places is 2.40 (do not write 2.4)

How do I round a number to a given significant figure?

• To find the first significant figure when reading from left to right, find the biggest place value that has a non-zero digit

  • The first significant figure of 3097 is 3

  • The first significant figure of 0.006207 is 6

    • The zeros before the 6 are not significant

    • The zero after the 6 is significant

• Count along to the right from the first significant figure to identify the position of the required significant figure 

  • Do count zeros that are between other non-zero digits

    • E.g. 0 is the second significant figure of 3097

    • 9 is the third significant figure of 3097

• Use the normal rules for rounding

• For large numbers, complete places up to the decimal point with zeros

  • E.g. 34 568 to 2 significant figures is 35 000

• For decimals, complete places between the decimal point and the first significant figure with zeros

  • E.g. 0.003 435 to 3 significant figures is 0.003 44

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

• If a question requires your answer to be an exact value

  • You can leave it as a simplified fraction

    • E.g.

  • You can leave it in terms of or a square root

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