Decimal Places & Significant Figures (SQA National 5 Maths): Revision Note

Rounding to a given place value

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

    • The number in the required place value increases by 1

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

    • The number in the required place value stays the same

  • 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

    • The number in the required decimal place increases by 1

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

    • The number in the required decimal place

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

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

  • Do not put any zeroes 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)

Rounding to significant figures

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

• 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 zeroes 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 zeroes 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 zeroes

  • 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 zeroes

  • 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

    • E.g. , or

  • If it is an exact decimal you can write it out without rounding it

    • E.g. 0.9375, or 850.25

• If the answer is not exact, an exam question will often state the required degree of accuracy for an answer

  • E.g. Give your answer to 2 significant figures

• If the degree of accuracy is not asked for, then 3 significant figures is usually a good choice 

  • All working and the final answer should show values correct to at least 4 significant figures

  • The final answer should then be rounded to 3 significant figures

• 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

• When calculating angles, rounding to 1 decimal place is usually a good choice (unless the question specifies otherwise)

  • An angle of 43.5789 will round to 43.6

  • An angle of 135.211... will round  to 135.2°

When might I need to estimate up or down?

• If a real life scenario is given, this may influence if you need to round up or down

• For example, if a class of 31 students requires at least 1 adult for every 10 children

  • 31 ÷ 10 = 3.1 adults are needed

  • 3 adults would not be enough, this would only be enough for 30 students

  • Therefore you would round up, to 4 adults

• Alternatively, consider a farmer filling crates that each hold 12 apples

  • How many crates can he fill if he has 50 apples?

    • 50 ÷ 12 = 4.16… crates will be filled

    • He cannot make a 5th full crate, as this would require 60 apples

    • Therefore, you would round down, to 4 crates