Significant Figures

Key ideas

Start counting at the first digit that isn't zero.

In 3048 the 1st significant figure is 3. In 0.0072 the 1st significant figure is 7.

How to round

1. Count the significant figures you need.

2. Look at the next digit: 5 or more, round up; 4 or less, leave it.

Keep the size

A rounded number must stay about the same size. Fill in with zeros up to the decimal point.

45 678 to 2 sig. figs is 46 000, not 46.

In context

Round to what makes sense: money to the nearest penny, people to whole numbers, measurements to a sensible accuracy.

Estimate by rounding each number to 1 significant figure.

34 572 → 35 000 (teal: the figures you keep; orange: the digit that decides)

Counting significant figures

Significant Figures

Finding the significant figures

Write down the first significant figure of (a) 5308 (b) 0.0624.(2 marks)

Whole number.5308: the first significant figure is 5✓¹

In plain EnglishIn a whole number, the first digit is usually the first significant figure.

Decimal.0.0624: the first significant figure is 6✓²

In plain EnglishZeros at the start don't count. Start counting at the first digit that isn't zero, which is 6.

Marking points

M1 5

M2 6

Rounding whole numbers

Significant Figures

Rounding a whole number

Round 34 572 to 2 significant figures.(2 marks)

Count 2 figures and look at the next one.34 572 next digit is 5: round up✓¹

In plain EnglishThe first two significant figures are 3 and 4. The next digit is 5, so the 4 rounds up to 5.

Fill with zeros.34 572 ≈ 35 000✓²

In plain EnglishPut zeros in the other places so the number stays the right size: about thirty-five thousand.

⚠ A common mistake: writing 35. That is far smaller than 34 572. Keep the zeros.

Marking points

M1 Rounds up

M2 35 000

Rounding decimals

Significant Figures

Rounding a decimal

Round 0.004 837 to 2 significant figures.(2 marks)

Find the first significant figure.0.004837 start at the 4✓¹

In plain EnglishThe zeros at the start don't count. The first two significant figures are 4 and 8. The next digit is 3.

Round.0.004 837 ≈ 0.0048✓²

In plain English3 is less than 5, so the 8 stays the same. We don't need zeros after the 8: they would not change the value.

Marking points

M1 Correct figures

M2 0.0048

Significant Figures

Rounding up past 9

Round 2.997 to 3 significant figures.(1 mark)

Round up.2.997 7: round up2.99 + 0.01 = 3.00✓¹

In plain EnglishRounding up the second 9 makes it 10, which carries over. To 3 significant figures, write 3.00: the zeros show the accuracy.

Marking points

M1 3.00

Rounding in context

Significant Figures

Rounding in context

A football stadium holds 48 726 people. A newspaper rounds this to 1 significant figure. What number do they print?(1 mark)

1 significant figure.48 726 8: round up48 726 ≈ 50 000✓¹

In plain EnglishThe first figure is 4 and the next is 8, so round up to 5 ten-thousands: 50 000.

Marking points

M1 50 000

Significant Figures

A calculator answer

A circle has area 50 cm². Its radius is √(50 ÷ 3.14) cm. Calculate the radius to 3 significant figures.(2 marks)

Use a calculator.50 ÷ 3.14 = 15.923…15.923… = 3.990 41…✓¹

In plain EnglishWork it out on the calculator. Don't round until the end.

Round.3.99041 0: leave itr = 3.99 cm✓²

In plain EnglishThe 4th figure is 0, so the 3.99 stays.

Marking points

M1 3.990…

M2 3.99 cm

Estimating

Significant Figures

Estimating

Estimate 487 × 31 by rounding each number to 1 significant figure.(2 marks)

Round each number.487 ≈ 50031 ≈ 30✓¹

In plain EnglishRound each number to 1 significant figure, so the sum is easy to do in your head.

Calculate.500 × 30 = 15 000✓²

In plain English5 × 3 = 15, then put the three zeros back on. The exact answer is 15 097, so the estimate is close.

Marking points

M1 500 × 30

M2 15 000

0 of 0 complete

Your turn

Calculator allowed. Type your rounded answer as a number, like 46000 or 0.0048. Remember to keep the zeros that hold the size of the number. Stuck? Tap Need a hint?