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.

 Measurements "Certain Plus One" or Signicant Digits Explaination 3.25cm 3.25 has 3 numerical digits therefore it contains 3 significant digits. The (3) and the (2) are two certain digits + one uncertain digit (5) add together to give 3 significant digits 25.180 25.180 has 5 numerical digits therefore it contains 5 significant digits. This value has 4 certain digits(2)(5)(1)(8). + one unterain digit (0)

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)

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.

 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:

 Measurements Certainty 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.

 Counted Values Defined Values 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.

 How many circles are there? Take a guess 2 and a little bit? 1.01? 3?

As you can see there can only be a exact value when you count.

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