### Significant Figures

Posted:

**Fri Oct 06, 2017 1:10 am**Based on a problem, how do we know how many sig figs we should round to?

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=8&t=21942

Page **1** of **1**

Posted: **Fri Oct 06, 2017 1:10 am**

Based on a problem, how do we know how many sig figs we should round to?

Posted: **Fri Oct 06, 2017 2:16 am**

For multiplication and division, the least number of significant figures in any number of the problem determines the number of significant figures in the answer.

For example

4.00 x 3.0 = 12

Since the number with the least sig figs in the problem is "3.0", which has 2 sig figs, the answer has 2 sig figs too.

For addition and subtraction, round the answer to the least number of places in the decimal portion of any number in the problem.

For example

3.50- 1.455= 2.05

The actual answer is 2.045, but since we have to round to the number of the problem with the least sig figs, which is 3.50, the answer has to be rounded to the nearest one hundredth.

For example

4.00 x 3.0 = 12

Since the number with the least sig figs in the problem is "3.0", which has 2 sig figs, the answer has 2 sig figs too.

For addition and subtraction, round the answer to the least number of places in the decimal portion of any number in the problem.

For example

3.50- 1.455= 2.05

The actual answer is 2.045, but since we have to round to the number of the problem with the least sig figs, which is 3.50, the answer has to be rounded to the nearest one hundredth.

Posted: **Fri Oct 06, 2017 9:47 am**

When you read the problem, there is usually a given mass/length/time.

Take part b of M7 for example: What mass of boron can be produced when

125kg of boron oxide is heated with 125kg of magnesium?

We are given 125kg, which has 3 sig figs. Hence, our answer will be reported in 3 sig figs.

This isn't the case sometimes, but usually holds true I think.

Take part b of M7 for example: What mass of boron can be produced when

125kg of boron oxide is heated with 125kg of magnesium?

We are given 125kg, which has 3 sig figs. Hence, our answer will be reported in 3 sig figs.

This isn't the case sometimes, but usually holds true I think.

Posted: **Fri Oct 06, 2017 2:21 pm**

Hello!

One very easy way to go about sig figs is to simply look at the amount of sig figs in the value that is given. For example, if you are given a problem of combustion that begins with 7.00 g of butane gas, the amount of sig figs for the answer will most likely be 3-- as there are 3 sig figs in "7.00." Of course, there are extenuating circumstances with this rule, but I have found that it is very helpful!

Hope this helps.

One very easy way to go about sig figs is to simply look at the amount of sig figs in the value that is given. For example, if you are given a problem of combustion that begins with 7.00 g of butane gas, the amount of sig figs for the answer will most likely be 3-- as there are 3 sig figs in "7.00." Of course, there are extenuating circumstances with this rule, but I have found that it is very helpful!

Hope this helps.

Posted: **Fri Oct 06, 2017 3:32 pm**

Generally, how many significant figures are needed when rounding percentages?

Posted: **Sat Oct 07, 2017 12:25 am**

Generally, you would round significant figures according to the value given in the question. For example, if the question gives you 3 sig figs, you would round your percentage to 3 sig figs. If there are 2 values in the question, you would choose the one with the least number of sig figs to base your answer on.

Posted: **Sat Oct 07, 2017 12:33 am**

Don't forget that 0's before the number are not significant and 0's in between and after the numbers are! For example, 0.0042 has only 2 sig figs, 403 has 3 sig figs, and 50.0 has 3 sig figs.

Posted: **Sun Oct 08, 2017 7:51 pm**

Additionally, do not forget there are certain rules when dividing by sigfig. The rule is your answer should have the same amount of sigfigs as the number with the least amount of significant figures!

Posted: **Sun Oct 08, 2017 8:48 pm**

how many significant digits are in the number 0.00678? would the two zeros before 678 be considered significant figures?

Posted: **Sun Oct 08, 2017 10:49 pm**

The two zero's after the decimal point are not significant figures. In this format, they are simply necessary for marking the order of magnitude. Without them, the number value would simply be different. It is always good to convert to scientific notation, a format that excludes significant figures to avoid confusion. Now, if the zero's were after the 8, and the number is of course transcribed with the correct number of significant figures, they would be considered significant, a sign of the accuracy of the measurement from which the number was obtained.