# Significant digits

#### Baby Einstein

Just Gen Chem I...but its about Sig Figs...know one seems to know the rules about which law to use when you have mixed equations

0.0001235 X 0.0012 + ( 5.48 - 0.004) X 9.1 + (8.2 x10 raised to the neg 6)

Give the correct answer with the correct number of sinigacant figures.

#### PRodQuanta

Just use a basic calculator. Once you've done that, your answer should only have only 7 digits. If it has more, round your smallest in value number until you reach 7 digits.

#### zefram_c

How do you get 7 digits?? Assuming uncertainty in the last digit of all given numbers, the most significant contribution comes from the term ( 5.48 - 0.004) X 9.1 - the uncertainty is on the order of 0.01*9.1 + 0.1*5.48 = roughly 0.5
So I would truncate the answer to the first digit past the decimal point... the terms with 10-6 and 0.000.. x 0.00... are 100% negligible.

#### Tide

Homework Helper
Round your answer off to the same number of significant digits as the element in your calculation that contains the fewest significant digits.

#### Baby Einstein

Now I'm really confused

#### Tide

Homework Helper
Your final numerical result cannot be more accurate than the least accurate of the items that go into your calculation.

#### Baby Einstein

:grumpy: Oh well, Iv'e got some type of block....to hell with this question.

#### Leong

$$0.001235X0.0012=1.5X10^{-7}$$ : 2 significant figures to follow the least one which is 0.0012 which has 2 significant figures.(Rule #1)

$$(5.48-0.004)=5.476 = 5.48$$ : 2 decimal places because the rest of the decimal places has no meaning since 5.48 has 2 decimal places only.(Rule #2)

5.48X9.1=50 ( 2 significant figures : Rule #1)

So,
$$1.5X10^{-7} + 50 + 8.2X10^{-6} = 50$$ ( 2 significant figures : Rule #2)

#### Baby Einstein

Thats what I thought 49.6540082 reported to two digits = 50, but my prof. says I'm wrong!

#### Alkatran

Homework Helper
Baby Einstein said:
Thats what I thought 49.6540082 reported to two digits = 50, but my prof. says I'm wrong!
I hate teachers like that. I've had to correct my teacher on how an electrical current works... he was completely backwards on parrallel/linear currents.

#### Tide

Homework Helper
Baby Einstein said:
Thats what I thought 49.6540082 reported to two digits = 50, but my prof. says I'm wrong!
Technically, your prof is correct. You need to display the trailing decimal point to indicate that you really do have two significant figures. Without it you are indicating the result is an integer which is "infinitely precise." Mathematically they are the same but the distinction is there when calculations involve measurements.

#### Baby Einstein

Thanks alot guys.

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