Precision and Accuracy are terms for quality of measurements. They have different meanings when used for scientific measurements.
Precision: how near repeated measurements of the same quantity agree with each other.
Example: If the repeated measurements of the same quantity agree with each other, the measurements have a high degree of precision.
Accuracy: how a measurement or multiple measurements agree with a true value (standard control).
In any science measurements, we usually strive for precision and accuracy. Precision depends on the fineness of calibration of the measuring device.
Example: A stopwatch versus a wristwatch. A stopwatch measures time more precisely than a wristwatch. Why?
- The difference that can be read on the stopwatch is about 0.01 seconds.
- The difference that can be read on the wristwatch is 0.5 seconds.
Errors in measurements can be caused by:
To view a brief video on precision and accuracy, click here.
The correct use of significant figures is essential in reporting any scientific measurements carried out in the lab. It is important to not that all digits obtained by measurement are significant. It is also important to know that the last digit to the right is an estimate.
To read more about significant figures, click here. There are several pages of this site, so be sure and click on Next at the bottom of each page.
Instructions for multiplying measurements:
Area = (length) (width)
Area = 20.14 in. × 9.45 in.
Area = 190.323 square inches
Question: Are we justified in reporting this six-digit number?
- Because our measurements of width and length contained only 4 and 3 significant figures respectively.
- Since the least precise figure in our multiplication contained only 3 significant figures, our answer must have only 3 significant figures.
- The correct value of the area is 190.00 square inches.
Note: Zeros used to show where a decimal point belongs are not significant.
Rules to ensure that your answers always contain the correct number of significant figures:
How to round off properly:
A scientific notation number has the general formula: N × 10exponent ; where N = a number between 1 and 10 and the exponent is a whole number that is the power to which a number is raised.
1,000,000 = 106
6 = the exponent
10 = the base
1,000,000 = 1 × 106
This is written by moving the decimal point six (6) places to the left and using the exponent 6.
1 million = 1,000,000 = 1 × 106
Types of Exponents
How to switch from scientific notation to ordinary figures:
You will need a scientific calculator for calculations involving numbers in scientific notation. The following keys must be used:
EE, EXP, or EEX (on the calculator)
Example: To enter the numbers 5.74 × 104
- First enter 5.74
- Press the EE, EXP, or EEX key
- Press 4
- The calculator will display:
5.74 × 1004
- Then proceed with any calculations with this number on the calculator.
Negative numbers can be entered into the calculator by following the steps below:
Try these for practice:
Round off to 2 significant digits
Positive Scientific Notation
Negative Scientific Notation