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Old Oct 9th 2017, 02:40 AM   #1
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Exclamation need help in physics

1- State how many significant figures are proper in the results of the following calculation:

(15.1)(0.20 - 30.05 + 170.2)

2- Cos 126.39

3- Soccer fields vary in size. A large soccer field is 90.3 m long and 83.1 m wide. What is its smallest dimension in inches? (Assume that 1 meter equals 3.281 feet.)

4- Solve: (1.6 x 102) / (3.5 x 103)

5- Solve: (4 x 10-1)2

6- Sin 109.65

Last edited by topsquark; Oct 9th 2017 at 11:06 AM. Reason: Too many questions
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Old Oct 11th 2017, 08:11 AM   #2
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Basically you should not include any more precision in the answer than is available in the question.

So if you have:
A = 1.2 / 2.3
the answer should not be quoted as 0.52173913

If we are rounding off the two input values, they might be anything from 1.15 to 1.25 and 2.25 to 2.35
Thus A can be anything from 1.15 / 2.35 = 0.4893617... up to 1.25 / 2.25 = 0.555555...
So in this case we can say only say the answer is about 0.52 (+/- 0.03)

Note the distinction between significant figures and decimal places.
In my example above the input values have 1 decimal place, but two significant figures,
(the output value has 2 significant figures and 2 decimal places).

It is unlikely that the input values are both at the extreme edges,
There is quite a sophisticated statistical analysis for error estimation (and thus provision of suitable numbers of significant figures)
However, as a pretty reliable rule of thumb,
the number of significant figures in the answer should not exceed the (minimum) number of significant figures in the question.

So the answer to A = 1.20 / 2.30 would be 0.522
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Last edited by Woody; Oct 12th 2017 at 05:29 AM.
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