Do you know what significant figure rules are? Do you know how to solve expressions with sig figs? Do you even know what a significant figure is, or how to calculate one? Whatever your answers, the significant figures calculator below is bound to be of assistance. It can help you to convert a number into a new number using significant figures. It will also solve expressions while helping you understand the rules at play.
What are Significant Figures?
Significant figures are numbers you can add to another number that add meaning to the value. To avoid repetition of particular figures, you can also round the numbers – but carefully. If you round too high or too low, you can impact the precision of the final value. If you require help with rounding for the most precise significant figure, you may want to use a rounding calculator.
What are the Rules of Significant Figures?
There are ways to work out what numbers you may consider to be significant, and those which are not. Use the set of rules below.
1. Any zero to the left of a non-zero number is not significant.
2. Placeholder trailing zeros are significant in numbers with a decimal point. In numbers without a decimal, this will depend on annotations and margins of error. This is often used to estimate population to the nearest thousand, for example.
3. If you have any zeros between non-zero numbers, they are significant.
4. Non-zero numbers are significant.
5. If there are fewer desired significant digits but more numbers, you round the numbers. In the case of 591,500, it becomes 592,000 with three significant figures, if trailing zeroes are considered to not be significant.
How to Use a Sig Fig (Significant Figure) Calculator?
A sig fig calculator is used in two ways – number rounding and arithmetic. Sig figs can also be calculated by hand with a significant figures counter.
You have 0.005289, but you want a number with two significant figures.
As the two zeros are trailing placeholders, they do not get counted.
You can round 5289 to two figures by rounding the 289 to 3. The number becomes 0.0053.
The same rule applies for non-decimal figures;
You have 1,528,529, but only want four significant figures. You can round the value up to one thousand, making the number 1,529,000.
In the case of scientific notation, you can use the same formula. However, you will have to use a scientific notation calculator, not a significant figure calculator.
The Additional Rules of Significant Figures
If you begin working with significant figures in the same formula as multiplication, division, addition, or subtraction, some new rules apply.
1. During addition and subtraction, multiplication and division, you can work out the calculations first then apply the standard significant figure rules at the end.
2. The final calculation shouldn’t have more significant figures than the value with the least amount.
An example:14.26 + 3.89 + 0.39. The figure 0.49 has the least number of significant figures, which means the final result must have two as well.
14.26 + 3.89 + 0.39 = 19
3. If you mix subtraction and addition with multiplication and division, you need to round the number at each step. Doing so can ensure you get the right number of significant figures at the end.
An example:14.26 + 3.89 x 0.39 to get 15.7771
That equals 14.26 + 1.5171
Then, round 1.5171 to two significant figures to get 14.26 + 1.50.
Add the two results – 14.26 + 1.50 to get 15.76, before rounding it to 16.
4. Defined, pure, and exact numbers do not affect the calculation’s accuracy. You can treat them as if they were significant numbers of infinite value. An excellent example of this is if you were to use a speed conversation calculator.
Let’s say you wanted to convert miles per hour to kilometers per hour. You would need to multiply the value by 1.6. The accuracy of the initial speed still determines the significant figures, such as:
14.28 x 1.6 = 22.98.