Measurement and Calculations con't
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Certainty
Rule for Multiplying and Dividng
Even when multiplying or dividing the certainty rule still applies. Although when you multiply 2 four-digit numbers together you can get a answer with 7 or 8 digit values, the rule of significant digit still applies. You must remember that the answer cannot contain be more certain that the original answer.
So in order
to determine the certainty when either multiplying or dividing the general rule
is:
When multiplying and/or dividing, the answer has the same number of signnificant digits as the measurement (one of the original values being multiplied) with the fewest number of significant digits.
As a result of this rule, the certainty of the answer will always depend on the value with the least significant digits.
| Sample Problem 1 Calculate the answer for the following question and state the correct certainty and units. Find the area of a triangle with a height of 9.7cm and a base width of 3.2cm Base
= 3.2 cm Area of Circle = 1/2 x base x height Area = 1/2 x 3.2cm x 9.7cm The original answer was 15.52 but seeing how the original value with the least significant digits was 3.2 (having 2 significant digits), the answer could only have 2 significant digits. **The answer must have the same number of significant digits as original value with the least significant digits, in this case 3.2 had the least. |
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Rounding
When rounding, you must be sure of how many significant digits you want. round to.
The Rule:
If the digit after the digit to be retained as the significant is 5 or greater, round up
| The original equations |
The pre-answer |
Number of significant digits needed |
Final Answer |
|
4.73 x 8.956 | 42.36188 |
We need 3 significant digits because the original value with
the least significant digits is 4.73. | Therefore
we round 42.36188 to 42.4 because we need 3 significant digits. |
| 18 x 56 | 1008 |
This is a exact value | 1008 |
| 000.0008 x 0.054 |
.000432 | We
need 1 significant digit because the original value with the least number of significant
is 000.0008 *Remember decimal and the leading zeros are not significant digits |
Therefore we round .000432 to .0004 because we need 1 significant
digits. |
Precision Rule for Adding and Subtracting
When adding or Subtracting there is another way to get a precise answer. This is call the precision rule; in the precision rule, precision is the last place value the last digit obtained from a measurement or calculation.
The Rule:
When adding and subtracting measured values of known precision, the answer has the same number of decimal places as the measure value with the fewest decimal places.
| The Explanation Let's say your given the values of 3.4mm, 4.56mm, 9.608mm and was asked to add these values up. You get the answer of 17.568mm, but we know that the answer can not be more precise than the measured value with the least precision. The measured with the least precision is 3.4mm (having only one decimal place) where 4.56mm have 2 decimal places and the value of 9.608mm has 3 decimal places. Therefore we must round the answer of 17.568mm to a value with only 1 decimal place. What is the answer?
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The following are more examples:
| The measured values (mm) |
The pre- answer | The
number of decimal places needed | The
answer |
| .008 + .0254
+.51223 | .54563mm |
The measured value with the least number of decimal places
is 0.008 having only 3 decimal places. | .546 |
| 2.12 -1.2 + 3 |
3.92 | The measured
value with the least number of decimal places is 3, having no decimal places |
4. |
On to the next topic: ::Speed::