Operations with Standard Form (Cambridge International IGCSE 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 box x 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 Hint **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 $\frac{1.275\times10^{6}}{3.4\times10^{-2}}$.

Write your answer in the form $A\times10^{n}$, where $1\leq A<10$ and $n$ is an integer.

Answer:

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

$\frac{1.275\times10^{6}}{3.4\times10^{-2}}=37500000$

Rewrite in standard form

$3.75\times10^{7}$