[artwill872]

I thought I understood this concept but I managed to get this problem wrong:

(1.245 x 243) + (421.1 x 0.02) =

This was my procedure:

(302.535) + (8.422)

the 2 in 302 seems like it should be the last significant figure because the smallest number being multiplied has 3 significant digits. The same reasoning applies to the 8.

( 303 )+( 8 ) = 311

Keep all three figures because when adding and subtracting you use the least amount of decimal places of the figures being added or subtracted. Here there are no numbers holding slots to the right of the decimal point.

311 = 3.11 x 10²

The correct answer according to my test answer key is 3.1 x 10².

Can someone please explain?

[Grundalizer]

you got 3.11 x 10²

Round down to two sig figs because 0.02 is two significant figures, which is the least accurate "measurement" in your original problem, therefore your answer must have two significant figures.  Remember- a 0 to the LEFT of the decimal place is NOT significant.

Hence 3.1 x 10²

[artwill872]

you got 3.11 x 10²

Round down to two sig figs because 0.02 is two significant figures, which is the least accurate "measurement" in your original problem, therefore your answer must have two significant figures.  Remember- a 0 to the LEFT of the decimal place is NOT significant.

Hence 3.1 x 10²

Ok, I'm still a bit confused.

I multiplied what was in each set of brackets as if they were isolated as my first step. (Should I not be thinking of it this way?) -- In the first set, I kept 3 significant figures from the product, as the number with the least amount of significant figures in that set was 3. In the second set, you are saying that I should have kept 2 significant figures, since the number with the least amount of significant figures in that set had 2.

But from here, wouldn't this mean that I will still be left with 3 significant figures because when adding or subtracting you keep only as many decimal places as the number with the least amount of decimal places? And the number 303 was left with zero numbers to the right of the decimal point.

If I have 303 as the product of my first set of brackets and 8.4 as the product of my second, then when I add them, the sum comes to 311.4 and I would remove the 4 because of what I stated above.

Where am I going wrong here?

[opti384]

you got 3.11 x 10²

Round down to two sig figs because 0.02 is two significant figures, which is the least accurate "measurement" in your original problem, therefore your answer must have two significant figures.  Remember- a 0 to the LEFT of the decimal place is NOT significant.

Hence 3.1 x 10²

Are you sure? Will 0.02 have two significant figures?

[rabolisk]

I agree with you, artwill872, and if you indeed got points off for sig figs, I would argue that you're correct.

[Borek]

(302.535) + (8.422)

( 303 )+( 8 ) = 311

This is actually wrong - you should not round before adding. You should add unrounded numbers to get 310.957 and round down then. Nonetheless 311 (three significant figures) is OK.

Don't worry too much about sig figs, they are faulty by design, and in practice never used after initial GenChem course.

[AWK]

If we are dealing with significant digits rigorously,  the correct answer is 3. x 10².
But if we are looking for the best approximation we use number 0.02 taken as rounded within limits 0.0195 and 0.0205. The result for both limits is correct within 2 significant digits.

[Borek]

If we are dealing with significant digits rigorously,  the correct answer is 3. x 10².

No. Rules for addition/subtraction are different from rules for multiplication/division

100.001 + 0.00000001 is 100.001 - six significant digits, not one.

[Grundalizer]

Quote from: Grundalizer on Yesterday at 02:13:01 PM
you got 3.11 x 102

Round down to two sig figs because 0.02 is two significant figures, which is the least accurate "measurement" in your original problem, therefore your answer must have two significant figures.  Remember- a 0 to the LEFT of the decimal place is NOT significant.

Hence 3.1 x 102

Are you sure? Will 0.02 have two significant figures?

Yes, why wouldn't it?  Zeros to the left of a decimal are not significant, zeros to the right of the decimal are significant.

[opti384]

0.02 will only have one sig fig number-- 2 itself.

[Borek]

Zeros to the left of a decimal are not significant, zeros to the right of the decimal are significant.

No. 0.0000001 is 1*10^-7 - assuming you are right first form has 7 sig figs, the other one one.