# Significant Figures rule confusion

Hello, i'm new here and thought that maybe I can learn a thing or two from this website.
Anyways, I need some help in the subject of Significant Figures. I'm getting confused with some of the rules. Here are the questions that i'm confused with.

Subtract and express to the correct significant figures

205.5
- 88
_____

Multiply and express to the correct significant figures

1005.2
x 1.7
______

-MysticalG

MysticalG said:
Hello, i'm new here and thought that maybe I can learn a thing or two from this website.
Anyways, I need some help in the subject of Significant Figures. I'm getting confused with some of the rules. Here are the questions that i'm confused with.

Subtract and express to the correct significant figures

205.5
- 88
_____

Multiply and express to the correct significant figures

1005.2
x 1.7
______

-MysticalG

With addition and subtraction, you round according to the element with the least amount of numbers beyond the decimal point. With multiplication and division, you round according to the element with the least amount of significant figures.

So would the first one be 207.5, or 208? The 88 has no decimals. :S

The second answer would be 1708.8?

Thanks.
-MysticalG

MysticalG said:
So would the first one be 207.5, or 208? The 88 has no decimals. :S

The second answer would be 1708.8?

Thanks.
-MysticalG

Saying the second answer would be 1708.8 would be implying that 1.7 has five significant digits, which is obviously incorrect. Take both numbers, and round according to the number with the LEAST amount of sigfigs.

I'm sorry, i'm confused by 'Take both numbers, and round according to the number with the LEAST amount of sigfigs.'

My apologies, if I am annoying you. I just don't get it, we learned this concept yesterday; and well I just don't want to be stuck in class.

Sorry for double posting, but can't anyone help :(

Take for example the following problem:

1.7800009 x 8.04

before rounding, you come up with 14.311207236...

Now, in the original problem, which number had the least amount of sigfigs? 8.04 did (only 3) compared to 1.7800009 (8 sigfigs). Because of this, you round your final answer to 3 sigfigs to match that of 8.04.

Understand?

Yeah.
So the answer for 1005.2 x 1.7 = 1.7 x 10^3?
Correct :D can anyone tell me if this is right? :|

1.7 x 103 looks good.

Integral
Staff Emeritus
Gold Member
MysticalG said:
Hello, i'm new here and thought that maybe I can learn a thing or two from this website.
Anyways, I need some help in the subject of Significant Figures. I'm getting confused with some of the rules. Here are the questions that i'm confused with.

Subtract and express to the correct significant figures

205.5
- 88
_____
If the 88 is the result of a measurement then it has only 2 sig figs, but if it is an integer resulting from counting then it has an infinite number of sig figs. So if the problem is that you have 88 beans that weigh 202.5g then the answer will have the same number of sig figs as the mass.
However if the 88 is the result of a measurement, as in if you measure the length of a rod to be 88cm and find its mass to be 1005.2 g, then the answer will have the same number of sig figs as the length.

Ok that covered things if the problem asked for multiplication or division, however it is a subtraction problem, so both the 88 and the 202.5 are representing the same type of quanity, therefore the 88 must represent a none integer, it has only 2 sig figs, so must the result.
Multiply and express to the correct significant figures

1005.2
x 1.7
______

The answer here will have the same number of sig figs as the least number of sig figs in the above 2 numbers.