Question

Perform the following calculations and round off the answers to proper significant

figures:

1. 9.82 ml + 10.0 ml + 9.980 ml =

2. (62.927 g/ml)(10.0 ml) =

Show calculation work

Answer 1

We follow the following rules to find signicficant figures of each of the given volume -

1. Non zero digits are always significant (Ex - 9.01) here 9 and 1 are significant

2. Any number of zeros between two significant digits are also significatn So, 9.01 has zero between 9 and 1 so, this 0 is also a significant digit.

3. Final zeroes after the decimal point at the end of the number are also significant. Ex 9.00 has 3 significant number 9 and two zeroes at the end of the decimal point but 900 has only one significant digit 9

Now, in 1 we have

9.82 ml ---- 3 significant figure

10.0 ----- 3 significant figure

9.980 ------ 4 significant figure

When we do addition we must add the numbers as it is and select the least no. of significant figures in the result by rounding off

So, 9.82 ml + 10.0 ml + 9.980 ml = 29.800 mL and selecting only the least no. of siginificant no. ( three in this case) we have final volume as 29.8 mL

2)

We have 62.927 g/ml ----- 5 significant figures

10.0 ---------------------- 3 significant figures

For division, we must divide the no. as it is and select the least no. of significant figures in the result by rounding off.

So, 62.927 g/ml /10.0 ml = 6.2927 g but it has 5 significant figures so, we start rounding off

6.2927 g -> 6.293 g (4 significant figures)-> 6.29 g (now it has 3 significant figures)

While rounding off if the last digit is greater than 5 we omit the last digit and increase the second last digit by 1, if if the last digit is lessthan 5 we just omit the last digit.