In science we have to be careful and consistent about how we report measurements.
Scientific measurements are reported so that every digit is certain except for the last digit, which is estimated.
We followed this convention
because the number of digits we report says something about the instrument we used to make the measurement.
For example, if we use the scale on the left, we could report the mass as 10.5 grams.
This scale can only tell the difference between 10.5 and 10.6 grams.
It cannot tell the difference between 10.49 grams and 10.50 grams.
If we use the scale on the right, however, we could report our mass as 10.4977 grams.
If we use this ruler to measure the black line, we know that the line is somewhere between zero and 10 units long.
We might guess the line is 7 units long. Or we might guess the line is 8 units long.
But this number is a guess, so we can only include this one digit.
If we use this ruler to measure the black line, we know the line is somewhere between 7 and 8 units long.
We might say the line is 7.7 units long or maybe 7.8 units long.
The ones digit is certain, but the tenths digit is estimated.
The way we report our number communicates something about the measurement we made.
It would be completely unreasonable for me to say the line is 7.77352948 units long if I measured it using this ruler.
When we make scientific measurements we can also consider the precision and accuracy of our measurements.
Precision is how close our measurements are to one another.
Accuracy, on the other hand, is how close our measurements are to the actual value of what we're measuring.
For example, student B has made precise measurements
because all four measurements are close to one another.
However since the average of the four measurements is far from the actual value of the mass, the measurements were not accurate.
Student C made both accurate and precise measurements.
The measurements are accurate because the average is very close to the actual mass
and the measurements are precise because the measurements are very close to one another
When we make scientific measurements we also considered the types of error that may be present.
Random error has the same probability of causing a measurement that is higher than the actual value
as lower than the actual value; the error is random.
If we repeat the experiment many times and average our measurements, the random error should average out of our measurement.
Systematic year on the other hand is a consistent error.
For example, if I were measuring a length but I was using a ruler that started at 2 inches instead of 0 inches,
all of my measurements would be off by 2 inches.
No matter how many times I repeat the experiment, my measurements would be off by 2 inches.
Systematic error does not average out with multiple trials.
So we want to be very careful in the way we design experiments and conduct them to minimize systematic error.