Question

Which is the sum of these values, to the appropriate number of significant digits?

a) 40.000
b) 41.000
c) 41.0000
d) 41.00

Answer 1

The sum of the values given to their appropriate significant digits is 40.69. This rounding is based on the least precise measurement, which in this case is to two decimal places.

Step-by-step explanation:

The sum of the values provided, rounded to the appropriate number of significant digits, is as follows:

1. (a) 31.57 (Since this is to two significant figures, the '7' in the hundredths place is the least significant figure.)
2. (b) 8.1649 (This value is to be rounded to three significant figures, so the '4' in the thousandths place is the least significant figure.)
3. (c) 0.051065 (When rounding to four significant figures, the last significant figure is the '1' in the ten-thousandths place.)
4. (d) 0.90275 (This value, rounded to four significant figures, would have '2' as the last significant figure.)

Adding these numbers up gives:

(a) 31.57
(b) 8.165 (rounded from 8.1649)
(c) 0.05107 (rounded from 0.051065)
(d) 0.9028 (rounded from 0.90275)

The sum of these numbers is 31.57 + 8.165 + 0.05107 + 0.9028 = 40.6888

However, when adding numbers with different precision, the result should not have more decimal places than the least precise measurement. Since the number with the least number of decimal places (31.57) has two decimal places, the sum should be rounded to two decimal places, giving 40.69.