Carry out the following calculation, making sure that your answer has the correct number of significant figures:

Question

7.61 g divided by 13.4 g - 8.17 g

Answer 1

Hi Dawson H.,

Xulai above answered almost correctly. But, an overriding rule in performing calculations of this type is, "preserve all data you are given, and round only once to express your final answer.

So: 7.61/(13.4-8.17) = 1.455... rounds to 1.5 . Same answer, in this case .... but not necessarily in general!

Rounding more than once is a tremendous no-no in data preparation in industries which are regulated, such as pharmaceuticals. And that includes data preparation "in parallel", for EACH reported datum.

Give you an example: a dosage form (a tablet) is found to contain 15.555 mg of an active ingredient, when it was labeled as containing 15 mg. Although the report may contain a statement of content in mg and also as %of label claim, each to be rounded to 1 decimal place, the mg would be reported (rounded) as 15.6 mg, but the %label claim would be calculated from the 15.555, as 103.7% (NOT 104.0% as 15.6 mg would imply). I can't tell you how much grief this causes beginning chemists (and this simple example is trivial compared to cases with multiple reported impurities, each with its own analytical criteria (limit of detection and limit of quantitation), but it's required (by government regulations), so that each datum reported is (each) as accurate as possible.

-- Cheers, --Mr. d.

Answer 2

If we assumed standard order of operations (divide, then subtract), we would have a mass divided by a mass, a unitless value, from which we would need to subtract mass, which we logically could not.

Therefore, we must first subtract the third mass (8.17 g) from the second (13.4 g). Subtraction and addition problems preserves significant digits up to the position of the final significant digit of the least precise value (13.4 g has a final digit of 4 in the tenths place, while 8.17 g has a 7 in the hundredths place). We perform the calculation and find the raw answer to be 5.23 g, but because our value with least precision is 13.4 g, we must round our answer to the nearest tenth of a gram, 5.2 g.

Subsequently, we divide 7.61 g by 5.2 g, and for division and multiplication problems, we keep significant digits equal to the value with the fewest overall digits, in this case, 5.2 g with two digits. 7.62 g divided by 5.2 g leaves a unitless (scalar) value of 1.463[461538 repeating], but since we can only preserve two significant digits, our final answer is "1.5".