Measurements and Calculations
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Certainty and Significant Digits
When you are talking about how certain you are about a measurement, this is called the degree of certainty or uncertainty. All measurements taken have some degree of certainty so scientist around the world have reached a international agreement about the correct way to record measurements.
The Rule:
Record all digits that are certain plus one uncertain digit. ("Certain plus one") all of these digits are called significant digits. A decimal has no bearing on how many significant digits there is, in fact ingnore the decimal.
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Measurements
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"Certain Plus One" or Signicant
Digits
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Explaination
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3.25cm
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3.25 has 3 numerical digits therefore it
contains 3 significant digits.
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The (3) and the (2) are two certain digits +
one uncertain digit (5) add together to give 3 significant
digits
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25.180
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25.180 has 5 numerical digits therefore it
contains 5 significant digits.
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This value has 4 certain digits(2)(5)(1)(8). +
one unterain digit (0)
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The Rule Con't:
All the digits in the value are significant digits except for any zeros (0) preceeding the value. (please go over the number below for explaination)
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As you can see there are 4 certain digits plus 1 uncertain digit totalling 5 significant digits. The leading zeros have no bearing on the number of significant digit. If the zero's are somewhere after the first significant number, then they count as a significant digit.
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As you can see the zeros (0's) after the first nine (9) are still included as significant digits. The uncertain digit can also be a zero, and it would also count as a signficant digit.. |
Another chart showing the correct way to record measurements:
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Measurements
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Certainty
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| 307.0 cm | 4 significant digits |
| 61 m/s | 2 significant digits |
| 0.03 m | 1 significant digit |
| 0.5060 km | 4 significant digits |
| 3.00 x 10 | 3 significant digits |
Counted or Defined Values
Counted or Defined values are exact values. Exact values contain an infinite number of significant digits. Defined values like 1000km/km or 60s/min are example of exact values.
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Counted Values
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Defined Values
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| 4 dogs | 1000/m/km |
| 10 CDs | 10 mm/cm |
| 3 Planes | 1h/60 min |
A person can not look at a parking lot and say there is 3 and a half cars parked (otherwise the person with the half car got ripped off). In this case it is a exact value of 3 cars.
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How many circles are there?
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Take a guess
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As you can see there can only be a exact value when you count.
Move on to: Measurements and Calculations con't