Standard Form

1. Standard Form What is it? Why is it useful?

2. Standard Form • Normal numbers are easy to deal with, we’re good at it • Sometimes we get numbers that are very very big or very very small. These can be difficult to use with normal numbers as you end up with so many zeroes. It’s easy to make a mistake.

3. Big Numbers • The speed of light is 300 million metres per second, or 300 000 000 m/s • This equates to twenty five thousand, nine hundred and twenty million kilometres per day, or 25 920 000 000 km/day • When you hear light years on TV, it means the distance that light travels in one year. That’s 946 080 000 000 kilometres in one year!

4. Tiny Numbers • Human hair 100 micrometres • Dust mite 200 micrometres • Lymphocyte 10 micrometres • Red blood cell 5 micrometres • E. Coli 2 micrometres • Staphylococcus 0.5 micrometres • Ebola virus 1000 nanometres

5. Tiny Numbers • Human hair 0.0001 m • Dust mite 200 micrometres • Lymphocyte 10 micrometres • Red blood cell 5 micrometres • E. Coli 2 micrometres • Staphylococcus 0.5 micrometres • Ebola virus 1000 nanometres

6. Tiny Numbers • Human hair 0.0001 m • Dust mite 0.0002 m • Lymphocyte 10 micrometres • Red blood cell 5 micrometres • E. Coli 2 micrometres • Staphylococcus 0.5 micrometres • Ebola virus 1000 nanometres

7. Tiny Numbers • Human hair 0.0001 m • Dust mite 0.0002 m • Lymphocyte 0.00001 m • Red blood cell 5 micrometres • E. Coli 2 micrometres • Staphylococcus 0.5 micrometres • Ebola virus 1000 nanometres

8. Tiny Numbers • Human hair 0.0001 m • Dust mite 0.0002 m • Lymphocyte 0.00001 m • Red blood cell 0.000005 m • E. Coli 2 micrometres • Staphylococcus 0.5 micrometres • Ebola virus 1000 nanometres

9. Tiny Numbers • Human hair 0.0001 m • Dust mite 0.0002 m • Lymphocyte 0.00001 m • Red blood cell 0.000005 m • E. Coli 0.000002 m • Staphylococcus 0.5 micrometres • Ebola virus 1000 nanometres

10. Tiny Numbers • Human hair 0.0001 m • Dust mite 0.0002 m • Lymphocyte 0.00001 m • Red blood cell 0.000005 m • E. Coli 0.000002 m • Staphylococcus 0.0000005 m • Ebola virus 1000 nanometres

11. Tiny Numbers • Human hair 0.0001 m • Dust mite 0.0002 m • Lymphocyte 0.00001 m • Red blood cell 0.000005 m • E. Coli 0.000002 m • Staphylococcus 0.0000005 m • Ebola virus 0.000001 m

12. Standard Form • Example: Express a light year in standard form Light year = 946 080 000 000 km • Example: Express the length of a single Ebola virus in standard form Ebola virus = 0.000001 m

13. Switching from Standard Form to normal numbers • We also need to be able to switch numbers in standard form to normal numbers. How? • Example: An adult has 2.5 x 1013 red blood cells in their body. Express this as a normal number. • Example: The weight of a single grain of rice is 2.5 x 10-5 kg. Express this as a normal number.

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

15. Calculating with Standard Form • Example: An adult typically has around 2.5 x 1013 red blood cells at any one time. If they measure 5 x 10-6 m in diameter, how far would they stretch if laid end to end? First things first, is it multiply or divide?

16. Calculating with Standard Form • Example: A typical helping of rice weighs 4.5 x 10-2 kg. If a typical grain of rice weighs 2.5 x 10-5 kg, how many grains of rice are there in a typical helping? First things first, is it multiply or divide?