1. Standard Form Objectives: B GradeUse standard index form with and without a calculator Prior knowledge: Understand : Positive index laws Simplifying fractions and dividing with decimals

2. Standard Form Standard form is used for writing either very large numbers or very small numbers by showing how many times that a single digit number would be either multiplied or divided by 10 Standard form is written in the form #.# × 10 x an integer between 1 and 9 the power of 10 Example 1: 700 can be written as 7 × 100 100 is 10 × 10 or 10 2 So now 700 can be written as 7 × 10 2 an integer between 1 and 9

3. Standard Form Example 2: 1400 can be written as 1.4 × 1000 1000 is 10 × 10 × 10 or 10 3 so now 1400 can be written as 1.4 × 10 3 Example 3: 0.0005 1 is 1 10 000 10 × 10 × 10 × 10 or 10 - 4 so now 0.0005 can be written as 5 × 10 - 4 Using negative index laws To help understand this think of the place value 1 10 000 can be written as 5 × 1 10 000

4. Now do these: Write these numbers in standard form: 1.40002.5003.70000 4.46 0005.466.2560 7.0.0078.0.00049.0.0035 10.0.42111.0.00005512.19 million 13. Avogadro’s number is 602 300 000 000 000 000 000 000. Express this in standard form. 14.A certain virus is 0.000 000 000 25 cm in diameter. Express this in standard form. Standard Form 4 × 10 4 7 × 10 - 3 5 × 10 2 7 × 10 4 4.6 × 10 4 4.6 × 10 1 2.56 × 10 3 4 × 10 - 4 3.5 × 10 -3 4.21 × 10 -1 5.5 × 10 -5 1.9 × 10 7 6.023 × 10 23 5.5 × 10 -10

5. Standard Form Calculations with Standard Form Work out the powers of 10 separately, Work out the number calculation Ensure the answer is in standard form Example 1: Calculate 4 × 10 4 × 2 × 10 3 10 4 ×10 3 = 10 7 4 ×2 = 8 Answer: 8 × 10 7

6. Standard Form Example 2: Calculate 8 × 10 5 × 7 × 10 4 10 5 ×10 4 = 10 9 8 ×7 = 56 56 × 10 9 This is not in standard form Answer: 5.6 × 10 10

7. Standard Form Example 3: Calculate 9 × 10 5 ÷ 3 × 10 2 10 5 ÷10 2 = 10 3 9 ÷ 3 = 3 3 × 10 3 Or it can be seen this way: 9 × 10 5 3 × 10 2 9 × 10 5 3 × 10 2 9 × 10 5 3 × 10 2 Cancelling common factors and applying the index law for division = 3 × 10 3

8. Standard Form Example 3: Calculate 1.8 × 10 6 ÷ 6 × 10 4 1.8 × 10 6 6 × 10 3 =18 × 10 5 6 × 10 3 = 3 × 10 2

9. Now do these: Calculate these and leave your answer in standard form: 1.5000 × 30002.60 000 × 5 000 3.0.000 07 × 4004.0.0007 × 0.000 01 5.8 000 ÷ 0.0046.0.000 033 ÷ 500 7.5.4 × 10 7 ÷ 2 × 10 3 8.4.8 × 10 2 ÷ 3 × 10 4 9. 1.8 × 10 4 ÷ 9 × 10 -2 10.5.4 × 10 -3 ÷ 2.7× 10 2 Standard Form 1.5 × 10 7 3.0 × 10 8 2.8 × 10 - 2 7.0 × 10 - 8 2 6.6 × 10 - 8 2.7 × 10 4 1.6 × 10 -2 2 × 10 5