Maths skills for chemistry · AQA and OCR A
Significant figures
Count significant figures, round a number and decide how many digits your answer needs. You can start here before Year 12.
Where would you like to start?
Quick check gives you 12 questions and a practice plan. Allow about five to ten minutes; take as long as you need.
Choose Practise to work on a particular skill. In Learn / check a number, I’ll show you what each digit means.
A calculator is useful for the two-step questions. Every formula you need is supplied.
Look at each digit
Type a number, including any final zeroes. I’ll show you which digits record its precision.
Decimals and e notation work here. For example, 4.50e-3 means 4.50 × 10⁻³.
What the digits tell you
A measurement carries information about its precision. A balance reading of 2.50 g records the mass to the nearest 0.01 g. Keep that final zero when you write the reading down.
Counting significant figures
Start at the first non-zero digit and count through the final written digit. In 0.00620, the digits 6, 2 and the final 0 give three significant figures. The earlier zeroes locate the decimal point.
Include zeroes between significant digits: 4.007 has four significant figures. In standard form, count the digits in the coefficient: 4.00 × 10⁵ has three.
A whole-number measurement such as 1200 needs context to establish its precision. Writing 1.2 × 10³, 1.20 × 10³ or 1.200 × 10³ makes two, three or four significant figures clear.
Rounding a number
Find the last significant digit you need to keep, then look at the next digit in the original value. A next digit of 5 or more rounds up. A smaller digit leaves the kept digit unchanged.
For example, 6.284 becomes 6.28 to three significant figures. 9.997 becomes 10.0. The zeroes in 10.0 show all three significant figures.
I’d always return to the original value for a new rounding question. Rounding in stages can change the answer.
Choosing the precision of a calculation
For the multiplication and division questions here, use the fewest significant figures among the measured inputs. For example, 3.42 × 1.5 = 5.13 on the calculator, so report 5.1.
A counted number or a defined unit conversion is exact. It leaves the measured precision unchanged: 35.0 cm³ = 0.0350 dm³.
Keep intermediate values in calculator memory. Round when the calculation is finished. In an exam, follow any instruction giving a particular precision. The rules here cover straightforward calculations; a full uncertainty calculation needs more information.
Decimal places, measurements and subtraction
Decimal places count positions after the decimal point. 12.30 has two decimal places and four significant figures.
For addition or subtraction of measured values, match the fewest decimal places among the inputs. 18.35 g − 6.20 g = 12.15 g. Both readings were recorded to two decimal places, so their difference keeps two.
Record digital readings at the instrument’s stated resolution. A balance reading in 0.01 g steps keeps two decimal places as its reading passes through 10 g or 100 g. The instrument’s overall uncertainty can involve other factors too.
Exam-board guidance: AQA mathematical requirements · OCR mathematical skills handbook (PDF).