Converting To & From Standard Form (Edexcel IGCSE Maths A (Modular))
Revision Note
Written by: Jamie Wood
Reviewed by: Dan Finlay
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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:
Where:
( is between 1 and 10)
( is positive) for large numbers
( 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
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
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 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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