1. ζ Standard Form Dr Frost
Objectives: Appreciate the need to put big and small numbers in a more readable form, how to write numbers in standard form, and calculations involving numbers in standard form.

2. Scale of the Universe

3. 𝑎×10𝑏 Standard Form Standard Form is useful for two reasons:
A number between 1 and 10 (excluding 10)
Any whole number (can be negative)
𝑎×10𝑏
(No need to copy this)
Standard Form is useful for two reasons:
It allows us to write really small or really big numbers concisely...
It allows us to compare small and big numbers.
Which is bigger?! 
Which is bigger? 
2.34 x 1014
2.34 x 1013

4. On a calculator?
4.86× ÷ 2.88× 10 9

5. Converting from Standard Form
We just consider how many times we’re multiplying or dividing by 10.
3 x 104
= 30000
1.24 x 105 = ? ?
Hint: Remember what happens when we have a negative index.
6 x 10-3
= 0.006
1.01 x 10-1
= 0.101 ? ?

6. Converting from Standard Form
We just consider how many times we’re multiplying or dividing by 10.
3.012 x 107
= 30,120,000
7.5 x 101
= 75 ? ?
8.31 x 100
= 8.31
2.4 x 10-6 = ? ?

7. Converting to Standard Form
How many times do we need to move the decimal point until we’re in the range 1 to 10? (excluding 10)
20000
= 2 x 104
0.0043
= 4.3 x 10-3 ? ?
931,000,000
= 9.31 x 108
= x 10-6 ? ?

8. Exercises
Express in standard form.
Express as a normal number.
300 =𝟑× 𝟏𝟎 𝟐
5,100 =𝟓.𝟏× 𝟏𝟎 𝟑
72,040.4=𝟕.𝟐𝟎𝟒𝟎𝟒× 𝟏𝟎 𝟒
119,988.7=𝟏.𝟏𝟗𝟗𝟖𝟖𝟕× 𝟏𝟎 𝟓
6,320,110=𝟔.𝟑𝟐𝟎𝟏𝟏×𝟏 𝟎 𝟔
8,108,136 =𝟖.𝟏𝟎𝟖𝟏𝟑𝟔× 𝟏𝟎 𝟔
77,012 =𝟕.𝟕𝟎𝟏𝟐× 𝟏𝟎 𝟒
1.72=𝟏.𝟕𝟐×𝟏 𝟎 𝟎
34.7=𝟑.𝟒𝟕× 𝟏𝟎 𝟐
0.001 =𝟏× 𝟏𝟎 −𝟑
=𝟑.𝟒× 𝟏𝟎 −𝟒
0.9 =𝟗× 𝟏𝟎 −𝟏
0.801 =𝟖.𝟎𝟏× 𝟏𝟎 −𝟏
=𝟏.𝟎𝟖𝟕× 𝟏𝟎 −𝟐
=𝟗× 𝟏𝟎 −𝟓
=𝟖.𝟔𝟑𝟐× 𝟏𝟎 −𝟓
0.11 =𝟏.𝟏× 𝟏𝟎 −𝟏 ?
3 x 102 =𝟑𝟎𝟎
4.71 x 103 =𝟒𝟕𝟏𝟎
2.401 x 105 =𝟐𝟒𝟎𝟏𝟎𝟎
7.42 x 106 =𝟕𝟒𝟐𝟎𝟎𝟎𝟎
x 103 =𝟏𝟏𝟏𝟏.𝟏
1.5 x 10-1 =𝟎.𝟏𝟓
3.01 x 10-4 =𝟎.𝟎𝟎𝟎𝟑𝟎𝟏
9.89 x 10-6 =𝟎.𝟎𝟎𝟎𝟎𝟎𝟗𝟖𝟗
3.456 x =𝟎.𝟎𝟎𝟎𝟎𝟎𝟎𝟑𝟒𝟓𝟔
1.234 x 10-1 =𝟎.𝟏𝟐𝟑𝟒 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

9. Testing your knowledge (vote with your diary)
200,000,000
20 x 107 
2 x 108  
2 x 107
32,000 
3.2 x 104
32 x 103  
3.2 x 105 9
9 x 10-1 
9 x 100  
9 x 101
0.0001
1 x 10-3 
1 x 10-4  
1 x 10-5
0.012
1.2 x 10-4 
12 x 10-3 
1.2 x 10-2 

10. Multiplying numbers in standard form
(2 x 103) x (4 x 104)
= 8 x 107 ? ?
(7 x 105) x (6 x 106)
= 42 x 1011
= 4.2 x 1012 ? ?

11. Multiplying numbers in standard form
(9 x 10-2) x (9 x 10-3)
= 81 x 10-5
= 8.1 x 101 x 10-5
= 8.1 x 10-4 ? ? ?

12. Dividing numbers in standard form
4× × 10 −2
= 0.5 x 107 ?
= 5 x 10-1 x 107 ?
= 5 x 106 ?

13. Dividing numbers in standard form
3× 10 −10 8× 10 −6
=0.375× 10 −4 ?
=3.75× 10 −5 ?

14. Questions
Edexcel GCSE Mathematics Textbook
Page Exercise 26B
Q4, 5
Page 432 – Exercise 26C

15. Adding and Subtracting?
=3000 ?
1× × =3× 10 3
4× × = 0.4× × =2.4× 10 4 ? ?

16. Examples
1.1× × =1.3× 10 5 ? ?
1.1× − 2× =9× 10 4 ?
5× × =5.02× 10 7 ?
6.2× 10 −2 + 3× 10 −3 =6.5× 10 −2 ?
9× × =2.09× 10 12 ?
3.2× 10 −4 − 5× 10 −5 =2.7× 10 −4