Standard Form

1. Standard Form Objectives: B Grade Use 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 the power of 10 #.# × 10x an integer between 1 and 9 an integer between 1 and 9 Example 1: 700 can be written as 7 × 100 100 is 10 × 10 or 102 So now 700 can be written as 7 × 102

3. Standard Form Example 2: 1400 can be written as 1.4 × 1000 or 103 1000 is 10 × 10 × 10 so now 1400 can be written as 1.4 × 103 To help understand this think of the place value 1 10 000 Example 3: 0.0005 can be written as 5 × 1 10 000 Using negative index laws 1 is 1 10 000 10 × 10 × 10 × 10 or 10-4 so now 0.0005 can be written as 5 × 10-4

4. Standard Form Now do these: Write these numbers in standard form: 1. 4000 2. 500 3. 70000 4. 46 000 5. 46 6. 2560 7. 0.007 8. 0.0004 9. 0.0035 10. 0.421 11. 0.000055 12. 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. 5 × 102 4 × 104 7 × 104 2.56 × 103 4.6 × 101 4.6 × 104 3.5 × 10-3 7 × 10-3 4 × 10-4 1.9 × 107 4.21 × 10-1 5.5 × 10-5 6.023 × 1023 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 × 104 × 2 × 103 104 ×103 = 107 4×2 = 8 Answer: 8 × 107

6. Standard Form Example 2: Calculate 8 × 105 × 7 × 104 105 ×104 = 109 8×7 = 56 56 × 109 This is not in standard form Answer: 5.6 × 1010

7. Standard Form Example 3: Calculate 9 × 105 ÷ 3 × 102 105 ÷102 = 103 9÷ 3 = 3 3 × 103 9 × 105 3 × 102 Or it can be seen this way: 9 × 105 3 × 102 Cancelling common factors and applying the index law for division 9 × 105 3 × 102 = 3 × 103

8. Standard Form Example 3: Calculate 1.8 × 106 ÷ 6 × 104 = 18 × 105 6 × 103 1.8 × 106 6 × 103 = 3 × 102

9. Standard Form Now do these: Calculate these and leave your answer in standard form: 1. 5000 × 3000 2. 60 000 × 5 000 3. 0.000 07 × 400 4. 0.0007 × 0.000 01 5. 8 000 ÷ 0.004 6. 0.000 033 ÷ 500 7. 5.4 ×107 ÷2 × 103 8. 4.8 × 102 ÷ 3 × 104 9. 1.8 ×104 ÷9 × 10-2 10. 5.4 × 10-3 ÷ 2.7× 102 1.5 × 107 3.0 × 108 2.8 × 10-2 7.0 × 10-8 2 6.6 × 10-8 2.7 × 104 1.6 × 10-2 2 × 105 2 × 105