standard form
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Standard FormStandard 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 FormStandard Form
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
Standard FormStandard 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
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.
Standard FormStandard Form
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
Standard FormStandard 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 FormStandard 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 FormStandard 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
9 × 105
3 × 102 Cancelling common factors and applying the index law for division
= 3 × 103
Standard FormStandard Form
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
Standard FormStandard Form
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
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