Sig Figs

[204863791]

Can anyone explain to me what sig figs are and how they work?

[Hannah_El-Sabrout_2K]

Sig figs are the digits which give us useful information about the accuracy of a measurement. The rules for the are that non-zero digits are always significant, any zeros between two significant digits are significant and a final zero/trailing zeros in the decimal portion are significant.

Examples:
So, 24.1 has three sig figs

0.00980 also has three sig figs (because the two zeros after the decimal point don't count - if you write it in scientific notation it might be easier to see, it is 9.80x10^-3)

When you add/subtract, the least amount of sig figs after the decimal count.
5.4 + 7.63 = 13.03 but you have to drop the 3 at the end because 5.4 only has one sig fig after the decimal (so the answer with the correct sig figs is 13.0

When you multiply/divide, the least amount of sig figs as a whole is what counts.
2.5 x 2.01 x 2.755 = 13.843875 but the answer with sig figs is 14 (because the 2.5 only has 2 sig figs)

I hope this was helpful!

[Amir Patel 1G]

There are additional significant figure examples about addition, subtraction, multiplication, and division, as well as rounding and logarithms on pages 122-123 in the Course Reader.

[gohar_mkrtchyan_2J]

0.00021 has two significant figures: 2 and 1 (the zeros before the 2 are not significant).
trailing zeros in a number containing a decimal point are significant (ex: 32.2100 has six sig figs.: 3, 2, 2, 1, 0, and 0).

[Michelle Steinberg2J]

Here are some helpful tips/rules for Sig Figs! :

1. All numbers 1-9 inclusive count as sig figs
2. Middle zeros are always significant
Ex. 409
3. Zeros before numbers 1-9 are not significant
Ex. 0.00390
The first 3 zeros are not significant.
4. Zeros after all numbers 1-9 are significant IF AND ONLY IF there is a decimal
Ex. 0.390
This example has 3 sig figs.

[jorineraymundo2h]

Our answer's sig fig should match the lowest number of sig fig in the problem.

[peytonruiz 1H]

I've always accepted and used sigfig rules, but why are they actually necessary? What is the purpose of sigfigs?

[Aleisa Quach 3C]

Sigfigs insure that the answer you get isn't more precise than that with which you start with. In solving these problems, the difference between the answer with and without sigfigs may seem small but on a larger scale can have a dramatic effect. Thus, sigfigs conserve the precision of the initial measurements in order to prevent such effects.

[Natalie LeRaybaud 1G]

So a little trick to remember sig figs is the PACIFIC/ATLANTIC rule.

If the decimal is PRESENT you start from the left side (Pacific) and go to the first non-zero number and count that one as well all the numbers after
Ex: 0.004670 would be 4 sig figs because the 1st non-zero number is 4 so you count the 4-6-7-and last 0
Ex: 0.29 would be 2 sig figs

If the decimal is ABSENT, you start from the right side (Atlantic) and go to three first non-zero number and count that one as well as all following numbers.
Ex: 789,000 would be 3 sig figs because the 9 is the 1st non-zero from the right side and the 7 and 8 follow
Ex: 45,290 would be 5 sig figs