Operations with Standard Form (Cambridge (CIE) IGCSE International Maths)

Revision Note

Author

Jamie Wood

Expertise

Maths

Operations with Standard Form

How do I perform calculations with numbers in standard form?

Your calculator can be used to help you carry out calculations with numbers written in standard form
Make use of brackets around each number, and use the $\times 10^{x}$ button to enter numbers in standard form
- e.g. $(3 \times 10^{8}) \times (2 \times 10^{- 3})$
- You can instead use the standard multiplication and index buttons
If the answer produced by your calculator is not in standard form, but the answer requires it:
- Either rewrite it using the standard process
  - e.g. 3 820 000 = 3.82 × 10⁶
- Or rewrite $a$ in standard form, then apply the laws of indices
  - e.g. 243 × 10²⁰ = (2.43 × 10²) × 10²⁰ = 2.43 × 10²²

Exam Tip

Calculations with numbers written in standard form will only appear on the calculator paper
- Therefore use your calculator wherever possible!
- However you can be asked to convert into or out of standard form in the non-calculator paper

Worked Example

Use your calculator to find $\frac{1.275 \times 10^{6}}{3.4 \times 10^{- 2}}$ .

Write your answer in the form $A \times 10^{n}$ , where $1 \leq A < 10$ and $n$ is an integer.

Input the calculation into your calculator, so it appears exactly as in the question
Your calculator may or may not present the answer in standard form
Copy the digits, especially the zeros, carefully

$\frac{1.275 \times 10^{6}}{3.4 \times 10^{- 2}} = 37 500 000$

Rewrite in standard form

$3.75 \times 10^{7}$

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