Q: Which of the following calculations demonstrates the correct application of significant figures in a multi-step operation?

$$ (2.34 \times 1.2) + 3.456 $$ rounded to one decimal place.

Question 1

When multiplying and dividing numbers, how do you determine the number of significant figures in the final answer?

Accepted Answer

Use the number with the least significant figures.

Question 2

Which of the following calculations is correctly rounded to the proper number of significant figures? $$ (3.16) 	imes (0.003027) 	imes (5.7 	imes 10^3$) $$

Accepted Answer

$$ 5.5 $$

Question 3

When adding or subtracting numbers, the final answer should be rounded based on:

Accepted Answer

The least number of decimal places.

Question 4

Given the calculation $$ 402.09 - 212.2 + 2.671 $$, what is the answer rounded to the correct number of decimal places?

Accepted Answer

$$ 192.6 $$

Question 5

In the order of operations (PEMDAS), which operation should be performed first?

Accepted Answer

Parentheses

Question 6

Calculate $$ [(1.89 	imes 10^4$) \div (3.005)] 	imes (5.21^2$) $$ and round to the correct number of significant figures.

Accepted Answer

$$ 6.18 	imes 10^4$ $$

Question 7

Which of the following is the correct result for $$ (6.404 	imes 2.91) \div (18.7 - 17.1) $$ with the proper number of significant figures?

Accepted Answer

$$ 11 $$

Question 8

A nurse needs to calculate a medication dose using $$ (1.7 	imes 10^4$) \div (2.63 	imes 10^3$) + 6.96 . $$What is the answer with the correct number of significant figures?

Accepted Answer

$$ 13.4 $$

Question 9

Which of the following best describes a significant figure?

Accepted Answer

Any digit that is measured or estimated in a measurement.

Question 10

What answer should be reported, with the correct number of significant figures, for the calculation $$ \frac{(42.00 - 40.914) \div (25.739 - 25.729)}{(11.50 - 1.001) + (0.00710 - 700.)} $$?

Accepted Answer

$$ -0.00100 $$

Question 11

A laboratory technician records the following measurements: 12.45 g, 12.4 g, and 12.452 g. Which measurement has the greatest number of significant figures?

Accepted Answer

12.452 g

Question 12

Which of the following calculations demonstrates the correct application of significant figures in a multi-step operation?

Accepted Answer

$$ (2.34 	imes 1.2) + 3.456 $$ rounded to one decimal place.

Question 13

A student calculates $$ (5.00 + 2.1) 	imes 3.00 . $$What is the correct answer with the proper number of significant figures?

Accepted Answer

$$ 21 $$

Question 14

Which step is necessary before rounding the final answer in a multi-step calculation involving both addition and multiplication?

Accepted Answer

Round only at the end of all operations.

Question 15

A chemist adds $$ 0.0030  g $$and $$ 0.002  g. $$What is the correct answer with the proper number of significant figures?

Accepted Answer

$$ 0.0050  g$$

Question 16

Which of the following is true about trailing zeros in a number like 1200?

Accepted Answer

They are significant only if there is a decimal point.

Question 17

A doctor orders a solution to be prepared by mixing $$ 15.0  mL $$and $$ 0.005  mL. $$What is the correct answer with the proper number of decimal places?

Accepted Answer

$$ 15.0  mL$$

Question 18

Which of the following is the correct result for $$ (8.829 - 6.5) \div (2.920) $$ with the proper number of significant figures?

Accepted Answer

$$ 0.80 $$

Question 19

If you perform $$ (12.0 	imes 0.25) + 3.00 $$, what is the correct answer with the proper number of significant figures?

Accepted Answer

$$ 6.0 $$

Significant Figures in Mathematical Operations: Multiplication, Division, Addition, and Subtraction

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