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1.2 Physical Quantities and Units -- Part 3
A store sells apples.
You purchase four bags of apples and weigh them each time.
The bag's expected value is 5 lbs.
The uncertainty is about 0.4 lbs.
The weight of the apple bag can be concluded.
The uncertainty in the weight remained the same if the bag of apples were half as heavy.
When calculating percent uncertainty, always remember to add the fraction by 100%.
If you don't do this, you won't have a percent value.
Anything calculated from measured quantities is uncertain.
The area of a floor calculated from the measurement of its length and width has an uncertainty because of uncertainties.
A coach bought a new stopwatch.
Runners on the track coach's team clock 100m of sprints.
The first- and second-place sprinters came in at the school's last track meet.
The uncertainty in the stopwatch is too great to differentiate between sprint times.
The precision of the measuring tool is an important factor in the accuracy of the measurement.
A precise measuring tool can measure values in very small amounts.
A ruler can measure length to the nearest millimeter, while a caliper can measure it to the nearest millimeter.
The caliper can measure extremely small differences in length, which makes it a more precise measuring tool.
The more precise the measuring tool is, the more accurate the measurement can be.
We can only list as many digits as we originally measured, when we express measured values.
If you use a standard ruler to measure the length of a stick, you can measure it to be.
The measuring tool you used was not precise enough to measure a hundredth of a centimeter.
The last digit in a measured value has been estimated by the person doing the measurement.
To determine the number of significant digits in a value, start with the first measured value at the left and count the number of digits through the last digit written on the right.
The measured value has significant figures.
The figures show the precision of the tool used to measure the value.
Special consideration is given to zeros.
The zeros in 0.053 are not significant because they are only placekeepers.
There are two significant figures.
The zeros in 10.053 are not placekeepers but are significant.
The style of writing numbers may affect the significance of the zeros in 1300.
The number could be known to the last digit or it could be a placekeeper.
1300 could have two, three, or four significant figures.
Zeros only serve as placekeepers.
The number of significant figures should be determined.
The number of significant digits in the final answer can't be greater than the number of significant digits in the least precise measured value.
The rules for multiplication and division are different from the rules for addition and subtraction.
The quantity with the least significant figures entering into the calculation should have the same number of significant figures.
The area of a circle can be calculated using the radius.
We can see how many significant figures the area has if the radius is only two.
A calculator that has an eight-digit output will give you 1.11.
The answer cannot contain more than the least precise measurement.
If you buy 7.56 kilo of potatoes at a grocery store, you will get a scale with a precision of 0.01 kilo.
The potatoes are measured by a scale with a precision of less than one kilo.
You measure the potatoes on a bathroom scale with a precision of 0.1 kilogram.
The least precise measurement is 13.7 kg.
Our final answer must also be expressed to the 0.1 decimal place because this measurement is expressed to it.
The answer is rounded to the tenths place, giving us 15.2 kilograms.
Most numbers are assumed to have three significant figures.
All worked examples use the same number of significant figures.
An answer given to three digits is based on input good to at least three digits.
The answer will have fewer significant figures if the input is less significant.
The number of significant figures is reasonable for the situation.
More accurate numbers are needed and more than three figures will be used in some topics.
It does not affect the number of significant figures in a calculation if a number is exact.
You can use the correct number of significant digits to express your answer.
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