Year 8 Standard Form Dr J Frost 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

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

Scale of the Universe

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 Which is bigger?!  Which is bigger? 2.34 x x Standard Form 

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

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

How many times do we need to move the decimal point until we’re in the range 1 to 10? (excluding 10) = 2 x 10 4 ? = 4.3 x ? 931,000,000 = 9.31 x 10 8 ? = x ? Converting to Standard Form

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

 200,000,000  20 x x 10 8  2 x ,000  3.2 x x 10 3  3.2 x  9 x x 10 0  9 x  1 x x  1 x  1.2 x x x Test Your Knowledge (Vote with your diary)

Standard Form on Your Calculator ? ? ? ? ?

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 we have to divide this by 10 so the number overall remains the same (and vice versa) Correcting numbers not in standard form

? ? ? ? ? More Examples:

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

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

8 x x 10 3 = 4 x 10 5 ? Dividing Numbers in Standard Form = 5 x x x ? = 0.5 x 10 7 ?

9 x x 10 6 = 4.5 x ? Test Your Understanding = 2.5 x x x ? = 0.25 x ?

Worksheet provided. Parts C and D Exercise