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Objectives:B Grade Use standard index form with and without a

calculator

Prior knowledge:

Understand :

Positive index laws

Simplifying fractions and dividing with decimals

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Standard form is used for writing either very large numbers orvery 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

the power of 10

Example 1: 700 can be written as 7 × 100

100 is 10 × 10 or 102

So now 700 can be written as 7 × 102

an integer between 1 and 9

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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

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

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.

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4 × 104

7 × 10-3

5 × 102 7 × 104

4.6 × 1044.6 × 101 2.56 × 103

4 × 10-4 3.5 × 10-3

4.21 × 10-15.5 × 10-5 1.9 × 107

6.023 × 1023

5.5 × 10-10

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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

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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

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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

9 × 105

3 × 102 Cancelling common factors and applying the index law for division

= 3 × 103

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Example 3:

Calculate 1.8 × 106 ÷ 6 × 104

1.8 × 106

6 × 103 = 18 × 105

6 × 103

= 3 × 102

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

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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