Question

1. Keeping in mind the rules for significant digits, if we multiply 11.55 by 2.5, how many significant digits are we allowed to keep?
A. 5
B. 2
C. 3
D. 4
2. Keeping in mind the rules for rounding, significant digits, and scientific notation, what is 975.0321/0.0003?
A. 3.250107 × 10^6
B. 3.3 × 10^6
C. 3.25 × 10^6
D. 3 × 10^6
E. 325010.7
3. Keeping in mind the rules for significant digits, find 0.00147 × 8.314 × 7.100?
A. 8.677 × 10^−2
B. 0.087
C. 8.68 × 10^−2
D. 8.7 × 1^02

Answer 1

1. For multiplication and division), we first compare the number of significant figure (let's call it SF later in the problem) that the factors have. The product will have the least numbers between them. So, for the case of 11.55 x 2.5, 11.55 has 4 SF while 2.5 has 2. So we choose the smallest which is 2 for this case. Hence, the answer is B. 2. Using the same rules as mentioned in Item 1, we first compare the number of SF in the numbers give. 975.0321 has 7 SF while 0.0003 has 1 (all zeroes not following a counting number are not significant). We now solve for the quotient and round it off to 1 SF. (975.0321/0.0003) = 3250107. Rounding it off, we have 3000000 or 3 x 10⁶. Thus, the answer is D. 3. The rules for multiplication still apply even for more than two factors. So, let's first take note of the SF present in each factor as shown below. 0.00147 = 3 SF 8.314 = 4 SF 7.100 = 4 SF (zeroes after a counting number in the decimal place are considered significant) From this, we can see that the product must round off to 3 SF. Multiplying the three numbers, we have 0.00147 x 8.314 x 7.100 = 0.086773218 So, the product rounded off to 3 SF is 0.0868 or 8.68 x 10⁻². So, the answer must be C.