Converting to & from Standard Form (AQA GCSE Maths) : Revision Note

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Converting to & from Standard Form

What is standard form and why is it used?

  • Standard form is a way of writing very large and very small numbers using powers of 10

  • This allows us to:

    • Write them more concisely

    • Compare them more easily

    • Perform calculations with them more easily

How do I write a number in standard form?

  • Numbers written in standard form are always written as:

a cross times 10 to the power of n

  • Where:

    • 1 less or equal than a less than 10 (a is between 1 and 10)

    • n greater than 0 (n is positive) for large numbers

    • n less than 0 (n is negative) for small numbers

How do I write a large number in standard form?

  • To write a large number such as 3 240 000 in standard form

    • Identify the value of a

      • 3.24

    • Find how many times you must multiply 3.24 by 10, to make 3 240 000

      • Count how many places you need to move the decimal point

      • We need to multiply by 10 six times

    • 3 240 000 = 3.24 × 10 × 10 × 10 × 10 × 10 × 10 = 3.24 × 106

How do I write a small number in standard form?

  • To write a small number such as 0.000567 in standard form

    • Identify the value of a

      • 5.67

    • Find how many times you must divide 5.67 by 10, to make 0.000567

      • Count how many places you need to move the decimal point

      • We need to divide by 10 four times

      • We are dividing rather than multiplying so the power will be negative

    • 0.000567 = 5.67 ÷ 10 ÷ 10 ÷ 10 ÷ 10 = 5.67 × 10-4

Examiner Tips and Tricks

  • On some calculators, typing in a very large or very small number and pressing box enclose equals will convert it to standard form

Worked Example

(a) Without a calculator, write 0.007052 in standard form.

Standard form will be written as a × 10n where a is between 1 and 10
Find the value for a

a = 7.052

The original number is smaller than 1 so n will be negative
Count how many times you need to divide a by 10 to get the original number

0.007052 = 7.052 ÷ 10 ÷ 10 ÷ 10   (3 times)

Therefore n = -3.

0.007052 = 7.052 × 10-3

(b) Without a calculator, write 324 500 000 in standard form.

Standard form will be written as a × 10n where a is between 1 and 10
Find the value for a

a = 3.245

The original number is larger than 1 so n will be positive
Count how many times you need to multiply a by 10 to get the original number

324 500 000  = 3.245 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10   (8 times)

Therefore n = 8

324 500 000 = 3.245 × 108 

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Jamie Wood

Author: Jamie Wood

Expertise: Maths Content Creator

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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