# Math

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How many significant figures does 22.0, 0.22, 22. , 0.022?

Im just confused as to the decimal addition to numbers and what the sig figs will be for them.

Thank you!!!

• Math -

I Googled "math significant figures" to get the information below.

The rules for significant figures are pretty straightforward:

Leading zeros are never significant digits. So in “0.0000024″, only the “2″ and the “4″ could be significant; the leading zeros aren’t.

Trailing zeros are only significant if they’re measured. So, for example, if we used the radius measurement above, but expressed it in micrometers, it would be 62,000 micrometers. I couldn’t claim that as 5 significant figures, because I really only measured two. On the other hand, if I actually measured it as 6.20 centimeters, then I could could three significant digits.

Digits other than zero in a measurement are always significant digits.

In multiplication and division, the number of the significant figures in the result is the smallest of the number of significant figures in the inputs. So, for example, if you multiple 5 by 3.14, the result will have on significant digit; if you multiply 1.41421 by 1.732, the result will have four significant digits.

In addition and subtraction, you keep the number of
significant digits in the input with the smallest number of decimal places.

That last rule is tricky. The basic idea is, write the numbers with the decimal point lined up. The point where the last significant digit occurs first is the last digit that can be significant in the result. For example, let’s look at 31.4159 plus 0.000254. There are 6 significant digits in 31.3159; and there are 3 significant digits in 0.000254. Let’s line them up to add:

31.4159
+ 0.000254
-------------
31.4162

The “9″ in 31.4159 is the significant digit occuring in the earliest decimal place – so it’s the cutoff line. Nothing smaller that 0.0001 can be significant. So we round off 0.000254 to 0.0003; the result still has 5 significant figures.

In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.

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