MATHEMATICS
3d
In mathematical and scientific work,
numbers can be very large or very small.
Speed of Light:
30 000 000 000 cm/s
Mass of the Earth:
5 980 000 000 000 000 000 000 000 kg.
Mass of an electron: 0.000 000 000 000 000 000 000 000 000 000 911 kg.
Capacitance in an electrical circuit:
Scientific Notation:
D x 10n 1
0.000 000 000 002 4 F
D
10 i.e. 7.23  10
5
A
Number is written as a product – two factors.
5
705 000 = 7.05 x 100 000 = 7.05 x (10 x 10 x 10 x 10 x 10) = 7.05  10
0.000 35 
3.5
1
 3.5 
 3.5 104
10000
10000
Move the decimal so there is only one digit left of the decimal.
To determine power of 10: count the number of places we move the decimal point.
Example: 705 000
Number is greater than 1
705 000.
Move decimal to the left
Exponent is positive
Move decimal 5 places to left. Exponent is +5.
7.05 105
Example: 0.000514
Number is between 0 and 1
0.000 514
Move decimal to the right
Exponent is negative
Move decimal 4 places to right. Exponent is – 4.
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5.14 104
MATHEMATICS
Change to scientific notation:
8. 0.004009
1. 0.82
9. 12002
2. 0.000 043
10. 0.0900
3. 9.45
11. 0.4275 x 10–1
4. 50 340
12. 73.5 x 102
5. 0.000 368 0
13. 0.0000913 x 104
6. 10
14. 489 x 10–5
7. 593.29
To change scientific notation to ordinary notation: Reverse the process.
6.46 x 104 = 6.46 x 10 000 = 64 600
Change the following to ordinary numbers:
15. 4.85 x 107 =
16. 7.8 x 100 =
17. 6.93 x 10-4 =
18. 1.0 x 101 =
19. 9.007 x 103 =
ANSWERS:
–1
1. 8.2 x 10
2. 4.3 x 10–5
3. 9.45 x 100
4. 5.034 x 104
5. 3.680 x 10–4
6. 1 x 101
13. 9.13 x 10–1
7. 5.9329 x 102
14. 4.89 x 10–3
8. 4.009 x 10–3
15. 48 500 000
9. 1.2002 x 104
16. 7.8
10. 9.00 x 10–2
17. 0.000 693
11. 4.275 x 10–2
18. 10
3
12. 7.35 x 10
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