Transcript AS/A Level Physics Presentation

SIGNIFICANT FIGURES
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The significant figure of a number are those digits that carry meaning contributing to its
precision.
The concept of significant digits is often used in connection with rounding.
The word significant means importance, so numbers which are at the beginning are
more important than others.
They represent the number of digits in a number, starting with the fist non zero number
and ending with any other number or trailing zero’s
They usually represent the accuracy and precision of a number.
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They are needed in calculations as they enhance accuracy and precision.
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The significant figure can tell us how good the data we have obtained is.
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They are essential in the engineering and science fields.
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Engineers who make calculations, use significant figures, especially when doing
conversions (e.g. Litres to ounces...)
In science, they increase the accuracy of an experiment and the results obtained.
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Consider the numbers:
100 grams
100. grams
100.00 grams
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The first number has only one significant figure (namely, the “1” in the beginning).
The second number has three significant figures (the decimal makes all three digits
significant, as we’ll discuss later).
The third number has five significant figures (as we’ll talk about later).
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The rules for identifying significant digits when writing or interpreting numbers are as
follows:
All non-zero digits are considered significant. For example, 91 has two significant digits
(9 and 1), while 123.45 has five significant digits (1, 2, 3, 4 and 5).
Zeros appearing anywhere between two non-zero digits are significant.
e.g. 101.12 has five significant digits: 1, 0, 1, 1 and 2.
Leading zeros are not significant. For example, 0.00052 has two significant digits: 5 and
2.
Trailing zeros in a number containing a decimal point are significant.
e.g. 12.2300 has six significant digits: 1, 2, 2, 3, 0 and 0.
The number 0.000122300 still has only six significant digits (the zeros before the 1 are
not significant).
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Generally, the same rules apply to numbers expressed in scientific notation:
When you write numbers in scientific notation, only the part before the
multiplication sign is counted in the significant figures.
For example:
0.00012 has two significant digits becomes 1.2×10−4
23900 has three significant figures, when we write it as 2.39 x 104
When there are zeros before the non-zero numbers, they are taken as
insignificant, when we write then in standard form.
e.g. 0.0000473= 4.73x10-5
So the zeros at the start are NOT counted as significant...
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To round to n significant digits:
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Start with the leftmost non-zero digit (e.g. the "1" in 1200, or the "2" in 0.0256).
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If the next number is 5 or greater, round up by adding 1
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If the next number is smaller than 5, do NOT round up and leave it the way it is.
e.g. If we want to round the number 5637 to 3 significant figures:
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Look at the number next to 3rd number.
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Its is greater than 5, so add 1...
Hence, it becomes 5640
But if it was 5634, then the 4th number is less than 5 so we don’t round up
Hence, it becomes 5630 to 3 S.f
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The rule for Addition and Subtraction:
Give the result the same number of digits after the decimal as the input with the fewest
such digits. E.g.
Addition:
89.332
+ 1.1
------90.432
Round to: 90.4
Subtraction:
66.59
- 3.113
------63.477
Round to:
63.48
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The rule for Multiplication and Division:
Give the result the same number of significant figures as the input with the fewest.
For example:
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(2.8) (4.5039) = 12.61092 = 13
Here, the number of significant figures, are given as the number with the least number
of significant figures. (this is the case if we are not giving a certain number of significant
figures to give our answers to)
Multiply the two numbers as they are, use the same rules for the final rounding
Similarly:
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(0.0154)/(883) = 0.00001744054 = 0.0000174 = 1.74 x 10-5
Divide the 2 numbers, then use the rules to round the final answer
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Write the following to 3 significant figures:
1)
6838= 684
2)
82074= 821
3)
274112= 274
4)
0.28742= 0.287
5)
0.00007839= 0.0000784
6)
100.80= 101.0
7)
179.99= 180.00
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