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![Page 1: Www.mathsrevision.com I. SCIENTIFIC NOTATION A METHOD OF DEALING WITH VERY LARGE AND VERY SMALL NUMBERS IN SCIENCE.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d785503460f94a5b785/html5/thumbnails/1.jpg)
ww
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A METHOD OF DEALING WITH
VERY LARGE AND VERY SMALL
NUMBERS IN SCIENCE
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Very large numbers!
BOOM!
How far?
92 000 000 miles
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Very small numbers!
How wide is an atom?
0.000 000 000 1 metres wide!
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Made up of three parts: the coefficient, the base and the exponent.
A. Writing Numbers in Scientific Notation
5.67 x 105 coefficient base exponent
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1. The coefficient must be between 1 and 9.9999999999999999999999999999999
2. The base must be 10
3. The exponent shows how many places the decimal moved.
5.67 x 105 coefficient base exponent
B. Scientific Notation Rules:
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Examples of Scientific Notation
363,000,000,000 = 3.63 x 1011
0.00035 = 3.5 x 10-4
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Numbers larger than 1, the exponent is positive Example: 8.38 x 105 = 838,000
Numbers less than 1, the exponent is negative Example: 5.03 x 10-3 = 0.00503
C. Scientific Notation Exponents
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92 000 000 79.2 10 ..
Add the decimal point
Between 1 and 10
The point moved 7 places
Move the point to get a number between 1 and 10
79.2 10 miles
D. Scientific Notation for Large Numbers
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0.000 000 000 1
101 10 .
The point moved 10 places. Negative sign for small numbers.
Move the point to get a number between 1 and 10
-101 10 metres wide
E. Scientific Notation for Small Numbers
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Examples of Scientific Notation
363,000,000,000 = 3.63 x 1011
0.00035 = 3.5 x 10-4
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a. 700 m c. 0.0054 kg
b. 38 000 m d. 0.000 006 87 kg
Practice – Convert to Scientific Notation
7 x 102 m
3.8 x 104 m
5.4 x 10-3 kg
6.87 x 10-6 kg
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=86 000 000 78.6 10
Zeros after the point aren’t needed.
The point moves 7 places to the right
8.60000000.
Hint:Add 7 zeros, although you probably won’t need them
all.
F. Changing back large numbers
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G.Changing back small numbers
= 0.000 00516
-65.16 10 5.16000000.
Hint:Add 6 zeros to the left of
the number.
-6 so remember to move point left for small numbers.
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a. 1.26 x 104 kg c. 9.02 x 103 kg
b. 5.36 x 10-2 m d. 7.6 x 10-5 m
Practice – Convert back to a number
12600 kg
0.0536 m
9020 kg
0.000076 m
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H. Multiplying using Scientific Notation
To multiply numbers in scientific notation, multiply the coefficients then add the exponents
Move the decimal point so that the number is in scientific notation
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Examples: Multiplying in Scientific Notation
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I. Dividing using Scientific Notation
To divide numbers written in scientific notation: – divide the coefficients then – subtract the exponent in the denominator
(bottom) from the exponent in the numerator (top) => “top – bottom” or “first – second”
Express the final answer in scientific notation
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Example: Dividing Numbers in Scientific Notation
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If you have to move the decimal to the LEFT, Add to the exponent
12.6 x 103 = 1.26 x 104
If you have to move the decimal to the RIGHT, Subtract from the exponent
0.902 x 104 = 9.02 x 103
Hint for converting an answer to scientific notation
LARS: Left Add, Right Subtract
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Practice – Multiplying and Dividing
1.2 x 1011
3 x 101 2 x 10-1
1.2 x 10-1