Question

how many significant figures digits should be used to report the answers to each of the following calculations? do not perform the calculations.
a. (2.7518 + 9.01 + 3.3349)/(2.1)
b. (2.775 × 1.95)/(0.98)
c. 12.0078/3.014
d. (0.997 + 4.011 + 3.876)/(1.86 × 10⁷)

Explanation:

Step1: Recall significant - figure rules for addition/subtraction

In addition and subtraction, the result should be rounded to the same number of decimal places as the number with the fewest decimal places in the values being added or subtracted.

Step2: Recall significant - figure rules for multiplication/division

In multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures in the values being multiplied or divided.

a. $(2.7518 + 9.01+3.3349)/(2.1)$

• First, consider the addition in the numerator: $2.7518 + 9.01+3.3349$. The number $9.01$ has two decimal - places. After addition, the result should be rounded to two decimal places.
• Then, for the division by $2.1$ (which has two significant figures), the final result should have two significant figures.

b. $(2.775\times1.95)/(0.98)$

• $2.775$ has four significant figures, $1.95$ has three significant figures, and $0.98$ has two significant figures. The result of the multiplication $2.775\times1.95$ should be rounded to three significant figures (since $1.95$ has the fewest significant figures among the multipliers), and then the division result should have two significant figures (because $0.98$ has two significant figures).

c. $12.0078/3.014$

• $12.0078$ has six significant figures and $3.014$ has four significant figures. The result of the division should have four significant figures.

d. $(0.997 + 4.011+3.876)/(1.86\times10^{7})$

• First, consider the addition in the numerator: $0.997 + 4.011+3.876$. The number $0.997$ has three decimal - places. After addition, the result should be rounded to three decimal places.
• Then, for the division by $1.86\times10^{7}$ (which has three significant figures), the final result should have three significant figures.

Answer:

a. 2 significant figures
b. 2 significant figures
c. 4 significant figures
d. 3 significant figures