Standard Standard FormFormWhat is it?What is it?

Why is it useful?Why is it useful?

Standard FormStandard Form

Normal numbers are easy to deal Normal numbers are easy to deal with, we’re good at itwith, we’re good at it

Sometimes we get numbers that Sometimes we get numbers that are are very very bigvery very big or or very very very very smallsmall. These can be difficult to . These can be difficult to use with normal numbers as you use with normal numbers as you end up with so many zeroes.end up with so many zeroes.

It’s easy to make a mistake.It’s easy to make a mistake.

Big NumbersBig Numbers

The speed of light is 300 million metres The speed of light is 300 million metres per second, or 300 000 000 m/sper second, or 300 000 000 m/s

This equates to twenty five thousand, nine This equates to twenty five thousand, nine hundred and twenty million kilometres per hundred and twenty million kilometres per day, or 25 920 000 000 km/dayday, or 25 920 000 000 km/day

When you hear light years on TV, it means When you hear light years on TV, it means the distance that light travels in one year.the distance that light travels in one year.

That’s 946 080 000 000 kilometres in one That’s 946 080 000 000 kilometres in one year!year!

Tiny NumbersTiny Numbers

Human hairHuman hair 100 micrometres100 micrometres Dust miteDust mite 200 micrometres200 micrometres LymphocyteLymphocyte 10 micrometres10 micrometres Red blood cellRed blood cell 5 micrometres5 micrometres E. ColiE. Coli 2 micrometres2 micrometres StaphylococcusStaphylococcus 0.5 micrometres0.5 micrometres Ebola virusEbola virus 1000 nanometres1000 nanometres

Tiny NumbersTiny Numbers

Human hairHuman hair 0.0001 m0.0001 m Dust miteDust mite 200 micrometres200 micrometres LymphocyteLymphocyte 10 micrometres10 micrometres Red blood cellRed blood cell 5 micrometres5 micrometres E. ColiE. Coli 2 micrometres2 micrometres StaphylococcusStaphylococcus 0.5 micrometres0.5 micrometres Ebola virusEbola virus 1000 nanometres1000 nanometres

Tiny NumbersTiny Numbers

Human hairHuman hair 0.0001 m0.0001 m Dust miteDust mite 0.0002 m0.0002 m LymphocyteLymphocyte 10 micrometres10 micrometres Red blood cellRed blood cell 5 micrometres5 micrometres E. ColiE. Coli 2 micrometres2 micrometres StaphylococcusStaphylococcus 0.5 micrometres0.5 micrometres Ebola virusEbola virus 1000 nanometres1000 nanometres

Tiny NumbersTiny Numbers

Human hairHuman hair 0.0001 m0.0001 m Dust miteDust mite 0.0002 m0.0002 m LymphocyteLymphocyte 0.00001 m0.00001 m Red blood cellRed blood cell 5 micrometres5 micrometres E. ColiE. Coli 2 micrometres2 micrometres StaphylococcusStaphylococcus 0.5 micrometres0.5 micrometres Ebola virusEbola virus 1000 nanometres1000 nanometres

Tiny NumbersTiny Numbers

Human hairHuman hair 0.0001 m0.0001 m Dust miteDust mite 0.0002 m0.0002 m LymphocyteLymphocyte 0.00001 m0.00001 m Red blood cellRed blood cell 0.000005 m0.000005 m E. ColiE. Coli 2 micrometres2 micrometres StaphylococcusStaphylococcus 0.5 micrometres0.5 micrometres Ebola virusEbola virus 1000 nanometres1000 nanometres

Tiny NumbersTiny Numbers

Human hairHuman hair 0.0001 m0.0001 m Dust miteDust mite 0.0002 m0.0002 m LymphocyteLymphocyte 0.00001 m0.00001 m Red blood cellRed blood cell 0.000005 m0.000005 m E. ColiE. Coli 0.000002 m0.000002 m StaphylococcusStaphylococcus 0.5 micrometres0.5 micrometres Ebola virusEbola virus 1000 nanometres1000 nanometres

Tiny NumbersTiny Numbers

Human hairHuman hair 0.0001 m0.0001 m Dust miteDust mite 0.0002 m0.0002 m LymphocyteLymphocyte 0.00001 m0.00001 m Red blood cellRed blood cell 0.000005 m0.000005 m E. ColiE. Coli 0.000002 m0.000002 m StaphylococcusStaphylococcus 0.0000005 m0.0000005 m Ebola virusEbola virus 1000 nanometres1000 nanometres

Tiny NumbersTiny Numbers

Human hairHuman hair 0.0001 m0.0001 m Dust miteDust mite 0.0002 m0.0002 m LymphocyteLymphocyte 0.00001 m0.00001 m Red blood cellRed blood cell 0.000005 m0.000005 m E. ColiE. Coli 0.000002 m0.000002 m StaphylococcusStaphylococcus 0.0000005 m0.0000005 m Ebola virusEbola virus 0.000001 m0.000001 m

Standard FormStandard Form

Example:Example:Express a light year in standard formExpress a light year in standard form

Light year = Light year = 946 080 000 000 946 080 000 000 kmkm

Example:Example:Express the length of a single Ebola Express the length of a single Ebola virus in standard formvirus in standard form

Ebola virus = Ebola virus = 0.000001 m0.000001 m

Switching from Standard Form Switching from Standard Form to normal numbersto normal numbers

We also need to be able to switch We also need to be able to switch numbers in standard form to normal numbers in standard form to normal numbers. How?numbers. How?

Example: Example: An adult has An adult has 2.5 x 102.5 x 101313 red blood cells red blood cells in their body. Express this as a normal in their body. Express this as a normal number.number.

Example: Example: The weight of a single grain of rice is The weight of a single grain of rice is 2.5 x 102.5 x 10-5-5 kg. Express this as a normal kg. Express this as a normal number.number.

Calculating with Standard Calculating with Standard FormForm

In addition to what we learned last In addition to what we learned last week, we often have to do week, we often have to do calculations with numbers that are in calculations with numbers that are in standard form.standard form.

Calculating with Standard Calculating with Standard FormForm

Example:Example:

An adult typically has around An adult typically has around

2.5 x 102.5 x 101313 red blood cells at any red blood cells at any one time. If they measure 5 x 10one time. If they measure 5 x 10--

66 m in diameter, how far would m in diameter, how far would they stretch if laid end to end?they stretch if laid end to end?

First things first, is it multiply or divide?

Calculating with Standard Calculating with Standard FormForm

Example:Example:

A typical helping of rice weighs A typical helping of rice weighs

4.5 x 104.5 x 10-2-2 kg. If a typical grain of kg. If a typical grain of rice weighs 2.5 x 10rice weighs 2.5 x 10-5-5 kg, how kg, how many grains of rice are there in a many grains of rice are there in a typical helping?typical helping?

First things first, is it multiply or divide?