In its simplest form, significant figures are a representation method. In every experiment and measurement, there are uncertainties arising from the measuring devices used, environmental factors and the nature of the system being studied. No measurement is/cannot be absolute certainty. When sharing our measurement with others, we also need to show this error/ambiguity in some way. You can use the sig fig calculator in just seconds with the tool we have designed just for you.
Table of Contents
What are the significant figures rules?
- Non-zero digits and zeros between other digits are significant. For example, the number 603902 has six significant digits.
- Leading zeros, that is, zeros before non-zero digits, are meaningless. For example, the three zeros at the beginning of the number 0.00427 are meaningless and the number has three significant digits.
- Some measurement results have an underlined or crossed-out number, which shows us that the numbers up to the underlined digit are significant. For example, in the number 1230000, the five numbers left until the zero in the fifth hundreds place are significant.
If there is a comma; If there are 10.00 commas, the trailing zeros are significant, so there are four significant digits in this number.
If there is no comma, for example, as in the number 55000, if there is no comma, the number can be rounded to 55000 and written as 5.5*10^4, so the trailing zeros are not significant and the number 55000 has two significant digits.
Why are significant figures important?
The correct number of digits must be included in the calculation results. By understanding and using significant numbers, you will be able to show how accurate a number is.
Measurement precision measures how close each measurement is to each other.
Measurement accuracy refers to the degree to which one or more measurements agree with the true or correct value.
How to add and subtract significant figures?
If you’re trying to add or subtract significant figures, use the rules below.
1. For addition and subtraction, count the significant digits in each number in the calculation.
2. Do the calculation normally
3. Your answer may not have more significant digits than the least significant digit in the problem.
How to multiply and divide by significant figures?
The rule for division and multiplication is that the last answer contains the same number of significant digits as the number with the least significant digits.
For multiplication and division, round your final answer to the level of the least significant digit in the problem.
How to use the Atlantic-Pacific rule for significant figures?
There are many rules regarding significant figures. However, it can be difficult to remember them all.
If a number has a decimal, use the Pacific rule.
The Pacific rule is this: If a number has a decimal place, start from the left half of the number and count numbers from the first non-zero number to the end of the number.
If a number has no decimal places, use the Atlantic rule.
The Atlantic rule is this: start on the right side of the number and count the numbers from the first nonzero number to the beginning of the number.
Significant Figures in Calculations
Example: Area of a Rectangle
A rectangular plate has a length of (21.3 ± 0.2) cm and a width of (9.80 ± 0.10) cm. Find the area of the plate and the uncertainty in the calculation (measuring error).
Solution: Area = lw = (21.3 ± 0.2) cm x (9.80 ± 0.1) cm = (21.3 x 9.80 ± 21.3 x 0.1 ± 9.80 x 0 ,2) cm2 = (209 ± 4) cm2
Note that the input data is given with only three significant figures. Therefore, we do not want our result to contain more significant figures. Do you see why we don’t need to multiply the 0.2 cm and 0.1 cm uncertainties?
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