Maths skills for chemistry · AQA and OCR A
Standard form and powers of ten
Write very large and very small numbers, use powers of ten and check your calculator entry. You can start here before Year 12.
Where would you like to start?
Quick check gives you 14 questions, then suggests what to practise. 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, you can change an exponent, compare the two forms and try calculator keys.
A scientific calculator is useful for the calculation questions. Those questions supply any chemistry formula they use.
Check a number
Type a number to see its ordinary and standard-form versions. Then change the exponent by one and see how the value changes.
Decimals, e notation and expressions such as 4.72 × 10^-5 work here.
What the exponent does
In 4.72 × 10³, 10³ is 1000, so the value is 4720. In 4.72 × 10⁻³, 10⁻³ is 1/1000, so the value is 0.00472.
I’d check the size first: does the coefficient need multiplying by a large number or by a fraction? That gives you the exponent’s sign. A negative exponent describes a small power of ten. A minus sign on the coefficient makes the whole value negative.
Putting the coefficient in range
Standard form uses one non-zero digit before the decimal point: 1 ≤ |coefficient| < 10, with a whole-number exponent. The vertical lines mean the coefficient’s size, including when the value is negative.
For 43.2 × 10⁻⁵, divide 43.2 by ten and multiply the power of ten by ten. You get 4.32 × 10⁻⁴, with exactly the same value.
10⁰ = 1, so 7.26 × 10⁰ is a valid way to write 7.26.
Keeping significant figures
0.0050 = 5.0 × 10⁻³. The final zero records the second significant figure in both forms.
A whole-number value such as 2500 needs context to establish its precision. 2.50 × 10³ shows three significant figures clearly. When converting it back to 2500, the original question still supplies that precision.
When rounding, check the coefficient again afterwards. 9.98 × 10⁴ to two significant figures becomes 1.0 × 10⁵.
Working with powers
Multiply powers by adding the exponents: 10³ × 10⁻⁵ = 10⁻². Divide by subtracting them: 10³ ÷ 10⁻⁵ = 10⁸. Raise a power by multiplying the exponents: (10³)² = 10⁶.
For multiplication and division in standard form, handle the coefficients and the powers, then adjust the coefficient into range. For addition and subtraction, first write both numbers using the same power of ten.
Use your calculator for the coefficients when needed. Keep its full result until you round the final answer.
Try your calculator entry
Find the EXP or ×10ˣ key on your calculator. For 4.72 × 10⁻⁵, enter 4.72, press that key once and enter −5. Your calculator may have a separate negative-sign key. Check its instructions for the exact sequence.
On an E-style display, 4.72E−5 means 4.72 × 10⁻⁵. In the practice keypad, E marks the exponent key.
Use these keys to practise entering one standard-form number. For a full calculation, use your own scientific calculator. Calculator displays often leave off final zeroes; use the original data and question to decide the written precision.
Exam-board guidance: AQA mathematical requirements · OCR mathematical skills handbook (PDF).