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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 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 #.# × 10x an integer between 1 and 9 Example 1: the power of 10 an integer between 1 and 9 700 can be written as 7 × 100 100 is 10 × 10 or 102 So now 700 can be written as 7 × 102 Standard Form Example 2: 1400 can be written as 1.4 × 1000 1000 is 10 × 10 × 10 or 103 so now 1400 can be written as 1.4 × 103 To help understand this think of the place value Example 3: 0.0005 1 10 000 can be written as 5 × Using negative index laws 1 is 1 10 000 10 × 10 × 10 × 10 1 10 000 or 10-4 so now 0.0005 can be written as 5 × 10-4 Standard Form Now do these: Write these numbers in standard form: 1. 4000 4 × 104 2. 500 5 × 102 4. 46 000 46 4.6 × 101 6. 5. 7. 4.6 × 104 0.007 7 × 10 3 8. 10. 0.421 11. 4.21 × 10 -1 3. - 70000 7 × 104 2560 2.56 × 103 3.5 × 10-3 0.0004 4 × 10 4 9. 0.0035 0.000055 19 million -5 5.5 × 10 12. 1.9 × 107 13. Avogadro’s number is 602 300 000 000 000 000 000 000. Express this in standard form. 23 6.023 × 10 14. A certain virus is 0.000 000 000 25 cm in diameter. Express this in standard form. -10 5.5 × 10 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 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 Standard Form Example 3: Calculate 9 × 105 ÷ 3 × 102 105 ÷102 = 103 9÷ 3 = 3 3 × 103 Or it can be seen this way: 9 × 105 3 × 102 9 × 105 3 × 102 Cancelling common factors and applying the index law for division 9 × 105 3 × 102 = 3 × 103 Standard Form Example 3: Calculate 1.8 × 106 ÷ 6 × 104 = 18 × 105 1.8 × 106 6 × 103 6 × 103 = 3 × 102 Standard Form Now do these: Calculate these and leave your answer in standard form: 1. 5000 × 3000 2. 1.5 × 107 3. 0.000 07 × 400 2.8 × 5. 10-2 8 000 ÷ 0.004 3.0 × 108 4. 6. 5.4 × 107 ÷ 2 × 103 1.8 × 104 ÷ 9 × 10-2 2 × 105 - 0.000 033 ÷ 500 6.6 × 10-8 8. 2.7 × 104 9. 0.0007 × 0.000 01 7.0 × 10 8 2 7. 60 000 × 5 000 4.8 × 102 ÷ 3 × 104 1.6 × 10-2 10. 5.4 × 10-3 ÷ 2.7× 102 2 × 105