1. Year 8 Standard Form Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 5 th March 2014 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. Associated Resources: Yr8_StandardFormQuestions.docx

2. 111111111.... x 1111111111... = Until you can’t enter any more digits. What do you notice in each case? Try these on your calculator…

3. www.scaleofuniverse.com Scale of the Universe

4. a  10 b A number between 1 and 10 (excluding 10) Any number (can be negative) (No need to copy this) Standard Form is useful for two reasons: 1.It allows us to write really small or really big numbers concisely... 2.It allows us to compare small and big numbers. 23400000000000023400000000000 Which is bigger?!  Which is bigger? 2.34 x 10 14 2.34 x 10 13 Standard Form 

5. We just consider how many times we’re multiplying or dividing by 10. 3 x 10 4 = 30,000 ? 1.24 x 10 5 = 124,000 ? 6 x 10 -3 = 0.006 ? Hint: Remember what happens when we have a negative index. 1.01 x 10 -1 = 0.101 ? Converting from Standard Form Count the number of decimal point jumps to check you’ve got it right.

6. 3.012 x 10 7 = 30,120,000 ? 7.5 x 10 1 = 75 ? 8.31 x 10 0 = 8.31 ? 2.4 x 10 -6 = 0.0000024 ? Check Your Understanding

7. 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 10 4 ? 0.0043 = 4.3 x 10 -3 ? 931,000,000 = 9.31 x 10 8 ? 0.000001001 = 1.001 x 10 -6 ? Converting to Standard Form

8. Worksheet provided. Part A and B (Part C if you finish) Exercise

9.  200,000,000  20 x 10 7 2 x 10 8  2 x 10 7 32,000  3.2 x 10 4 32 x 10 3  3.2 x 10 5 9  9 x 10 -1 9 x 10 0  9 x 10 1 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 Test Your Knowledge (Vote with your diary)

10. Standard Form on Your Calculator ? ? ? ? ?

11. If the number at the front is not between 1 and 10 (excluding 10), it’s not in standard form. We can fix this! 200 x 10 4 = 2 x 10 2 x 10 4 = 2 x 10 6 ? ? Step 1: Convert the number at the front to standard form. Step 2: Use laws of indices to simplify. A faster alternative is this: Each time we multiply this number 10......we have to divide this by 10 so the number overall remains the same (and vice versa) Correcting numbers not in standard form

12. ? ? ? ? ? More Examples:

13. (2 x 10 3 ) x (4 x 10 4 ) = 8 x 10 7 ? ? (7 x 10 5 ) x (6 x 10 6 ) = 42 x 10 11 = 4.2 x 10 12 ? ? Multiplying Numbers in Standard Form

14. (9 x 10 -2 ) x (9 x 10 -3 ) = 81 x 10 -5 = 8.1 x 10 -4 ? ? Test Your Understanding (7 x 10 7 ) x (2 x 10 -3 ) = 14 x 10 4 = 1.4 x 10 5 ? ?

15. 8 x 10 8 2 x 10 3 = 4 x 10 5 ? Dividing Numbers in Standard Form = 5 x 10 6 4 x 10 5 8 x 10 -2 ? = 0.5 x 10 7 ?

16. 9 x 10 3 2 x 10 6 = 4.5 x 10 -3 ? Test Your Understanding = 2.5 x 10 12 2 x 10 8 8 x 10 -5 ? = 0.25 x 10 13 ?

17. Worksheet provided. Parts C and D Exercise