1. Standard Form

2. Starter How to say big numbers!
What could each of these numbers represent? How do you even say them? Why might they be annoying to use?
37,200,000,000,000
Estimate for the number of cells in the human body
“Thirty-seven trillion, two hundred billion”
b) 38,000,000,000,000,000m
Rough distance to Alpha Centauri in metres (third nearest star to Earth)
“Thirty-eight quadrillion”
c) 1,989,000,000,000,000,000,000,000,000,000kg
Estimated weight of the sun in kilograms
“One nonillion, nine hundred and eighty-nine octillion”

3. Standard Form You may have seen Standard Form in Science
It is a way of writing very big or very small numbers a bit more easily
For example
 38,000,000,000,000,000m
 This is the distance from Earth to Alpha Centauri m
 The width of a some molecules

4. This is 5000 in Standard Form as the first number is between 1 and 10!
Standard Form numbers are written as a number between 1 and 10 (not including 10), multiplied by a power of 10
 Let’s the number 5000 as an example:
5000
= 5000 x 1
= 5000 x 100
Using powers of 10
= 500 x 10
= 500 x 101
This is 5000 in Standard Form as the first number is between 1 and 10!
= 50 x 100
= 50 x 102
= 5 x 1000
= 5 x 103
= 0.5 x 10000
= 0.5 x 104
= 0.05 x
= 0.05 x 105

5. Standard Form 46300 = 46300 x 1 = 46300 x 100 = 4630 x 10 = 4630 x 101
Standard Form numbers are written as a number between 1 and 10 (not including 10), multiplied by a power of 10
 Let’s the number as an example:
46300
= x 1
= x 100
Using powers of 10
= 4630 x 10
= 4630 x 101
= 463 x 100
= 463 x 102
This is in Standard Form as the first number is between 1 and 10!
= 46.3 x 1000
= 46.3 x 103
= 4.63 x 10000
= 4.63 x 104
= x
= x 105

6. Standard Form 3 8 The distance from Earth to the Moon is: 3.8 x 105 km
Write this in full:
So the answer in full is 380,000km 3 8

7. Standard Form 3 6 5 The Empire state building weighs approximately:
3.65 x 108 kilograms
Write this in full:
So the answer in full is 365,000,000kg 3 6 5

8. Standard Form 2 3 4 Write in Standard Form: 23,400,000,000m
Write this in full:
The decimal has to ‘move’ 10 places to make the first number between 1 and 10
 2.34 x 1010 2 3 4

9. Standard Form
You also need to be able to deal with Standard Form with very small numbers!
What might these represent? m
The width of a DNA strand (3 nanometres)
b) m
 The size of a water molecule (280 picometres)

10. Write as multiplications
Standard Form
Standard Form numbers are written as a number between 1 and 10 (not including 10), multiplied by a power of 10
 Let’s the number as an example:
0.0007
= ÷ 1
= ÷ 100
= x 100
Write as multiplications
÷ 103 = x 10-3
= ÷ 10
= ÷ 101
= x 10-1
Using powers of 10
= ÷ 100
= ÷ 102
= x 10-2
= 0.7 ÷ 1000
= 0.7 ÷ 103
= 0.7 x 10-3
= 7 ÷ 10000
= 7 ÷ 104
= 7 x 10-4
= 70 ÷
= 70 ÷ 105
= 70 x 10-5
This is in Standard Form as the first number is between 1 and 10!

11. Standard Form
Write as a decimal number;
8 x 10-4  8

12. Standard Form Write as a decimal number; 6.51 x 10-8  0.0000000651 66 5 1

13. Standard Form
Write as Standard Form;
 7.3 x 10-5 7 3

14. The scale of the universe – a big range of Standard Form numbers!
Plenary
The scale of the universe – a big range of Standard Form numbers!

15. Summary We have learnt what Standard Form is, and where it is used
We have learnt how to write Standard Form numbers as ordinary ‘decimal’ numbers
We have seen an awesome webpage of the very big and the very small!