Standard Form

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”

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 0.000000000000144m  The width of a some molecules

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 100000 = 0.05 x 105

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 46300 as an example: 46300 = 46300 x 1 = 46300 x 100 Using powers of 10 = 4630 x 10 = 4630 x 101 = 463 x 100 = 463 x 102 This is 46300 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 = 0.463 x 100000 = 0.463 x 105

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

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

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

Standard Form You also need to be able to deal with Standard Form with very small numbers! What might these represent? 0.000000003m The width of a DNA strand (3 nanometres) b) 0.00000000028m  The size of a water molecule (280 picometres)

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 0.0007 as an example: 0.0007 = 0.0007 ÷ 1 = 0.0007 ÷ 100 = 0.0007 x 100 Write as multiplications ÷ 103 = x 10-3 = 0.007 ÷ 10 = 0.007 ÷ 101 = 0.007 x 10-1 Using powers of 10 = 0.07 ÷ 100 = 0.07 ÷ 102 = 0.07 x 10-2 = 0.7 ÷ 1000 = 0.7 ÷ 103 = 0.7 x 10-3 = 7 ÷ 10000 = 7 ÷ 104 = 7 x 10-4 = 70 ÷ 100000 = 70 ÷ 105 = 70 x 10-5 This is 0.0007 in Standard Form as the first number is between 1 and 10!

Standard Form Write as a decimal number; 8 x 10-4  0.0008 8

Standard Form Write as a decimal number; 6.51 x 10-8  0.0000000651 6 6 5 1

Standard Form Write as Standard Form; 0.000073  7.3 x 10-5 7 3

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!

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!