Sheet № 134 · Foundation + Higher · AQA · Edexcel · OCR
Calculating with Standard Form –
Calculating with standard form extends the basics of writing numbers in standard form to performing arithmetic with them. You may need to multiply, divide, add, or subtract numbers in standard form on both Foundation and Higher GCSE Maths papers.
§Key definitions
Question:
Calculate (3 × 10⁴) × (2 × 10³). Give your answer in standard form.
Answer:
4.82 × 10⁶
Q1 (Foundation):
Calculate (5 × 10³) × (4 × 10²). Give your answer in standard form.
Q2 (Foundation):
Calculate (9.6 × 10⁷) ÷ (3.2 × 10⁴). Give your answer in standard form.
Q3 (Higher):
Calculate (7.1 × 10⁸) − (4.6 × 10⁷). Give your answer in standard form.
§Formulas to memorise
Multiplying: (a × 10^m) × (b × 10^n) = (a × b) × 10^(m+n)
Dividing: (a × 10^m) ÷ (b × 10^n) = (a ÷ b) × 10^(m−n)
Adding/subtracting: convert to the same power of 10, then add or subtract the A values
Worked example
Calculate (3 × 10⁴) × (2 × 10³). Give your answer in standard form.
Working:
⚠ Common mistakes
- ✗Adding powers when adding or subtracting numbers. You add powers only when multiplying. For addition/subtraction, you must convert to the same power first.
- ✗Forgetting to adjust when A falls outside the valid range. If multiplying gives 15 × 10⁸, this is not standard form. Write it as 1.5 × 10⁹.
- ✗Subtracting powers in the wrong order when dividing. Always subtract the second power from the first: m − n, not n − m.
✦ Exam tips
- →On calculator papers, use the EXP or ×10^x button — do not type × 10 ^ manually, as this can cause errors.
- →Always state your final answer in standard form unless the question asks for an ordinary number.
- →Double-check that 1 ≤ A < 10 in your final answer.