Q: Which of the following calculations requires you to round the final answer to the least number of significant figures?

$$(2.349 \times 31.39)(4.909 - 4.354)$$

Question 1

When performing the calculation $$28.4445 + 42.7 + 0.259$$, which rule should you use to determine the number of decimal places in the final answer?

Accepted Answer

Use the number with the fewest decimal places.

Question 2

Calculate $$5.159 + 82.3 - 0.024 - 3.00$$ and round your answer to the correct number of significant figures.

Accepted Answer

$$84.4$$

Question 3

Which of the following best explains why $$2.404 + 9.848 	imes 5.928 - 5.434 is $$calculated as $$7.27$$?

Accepted Answer

The answer is rounded to the least number of decimal places after addition/subtraction and to the least number of significant figures after multiplication.

Question 4

A student calculates $$(2.349 	imes 31.39)(4.909 - 4.354)$$ and gets $$133. $$Which rule did they use to round their answer?

Accepted Answer

They rounded to the least number of significant figures present in any number used.

Question 5

Given the calculation $$-27.89 \div 2.2683 - 1.791 + 52.865$$, what is the correct answer rounded to the appropriate number of significant figures?

Accepted Answer

$$-5.6$$

Question 6

Which of the following calculations requires you to round the final answer to the least number of significant figures?

Accepted Answer

$$(2.349 	imes 31.39)(4.909 - 4.354)$$

Question 7

A nurse needs to prepare a solution by mixing $$28.4445 mL$$, $$42.7 mL$$, and $$0.259 mL of $$three different chemicals. What is the total volume, rounded correctly?

Accepted Answer

$$71.4$$

Question 8

If you multiply $$2.404 by$$ $$9.848$$ and then subtract $$5.434$$, what is the correct answer with proper significant figures?

Accepted Answer

$$18.2$$

Question 9

Which of the following best describes the process for determining the number of significant figures in the result of $$-27.89 \div 2.2683$$?

Accepted Answer

The result should have as many significant figures as the number with the fewest significant figures.

Question 10

A chemist adds $$5.159 g$$, $$82.3 g$$, and $$0.024 g$$, then subtracts $$3.00 g. $$What is the correct mass, rounded to the proper decimal place?

Accepted Answer

$$84.4 g$$

Question 11

In a real-world scenario, a pharmacist calculates $$(2.349 	imes 31.39)(4.909 - 4.354) to $$determine the amount of a compound needed. If the numbers have 4, 4, 3, and 3 significant figures respectively, how many significant figures should the final answer have?

Accepted Answer

3

Question 12

A student calculates $$2.404 + 9.848 	imes 5.928 - 5.434$$ and gets $$7.27. $$Which of the following best explains the correct use of significant figures and decimal places in this calculation?

Accepted Answer

Multiplication/division is rounded to the least number of significant figures, and addition/subtraction is rounded to the least number of decimal places.

Question 13

Which of the following is the correct answer for $$(2.349 	imes 31.39)(4.909 - 4.354)$$, rounded to the correct number of significant figures?

Accepted Answer

$$133$$

Question 14

A laboratory technician needs to divide $$-27.89 by$$ $$2.2683$$, subtract $$1.791$$, and add $$52.865. $$What is the final answer, rounded to the correct number of decimal places?

Accepted Answer

$$-5.6$$

Question 15

Which of the following is the correct process for rounding the result of $$2.404 + 9.848 	imes 5.928 - 5.434$$?

Accepted Answer

First, perform the multiplication and round to the least number of significant figures, then perform the addition and subtraction and round to the least number of decimal places.

Question 16

A student is asked to solve $$2.404 + 9.848 	imes 5.928 - 5.434 in $$two different ways and gets $$7.27$$ and $$6.05. $$What is the most likely reason for the difference?

Accepted Answer

They performed the operations in a different order.

Question 17

If you are given the numbers $$2.404 (3 $$decimal places), $$9.848 (3 $$decimal places), and $$5.928 (3 $$decimal places), and you multiply $$9.848 	imes 5.928$$, how many significant figures should your answer have?

Accepted Answer

4

Question 18

A real-world application: A doctor prescribes a medication that requires mixing $$2.349 mg of $$one compound with $$31.39 mg of $$another, and then multiplying by the difference between $$4.909$$ and $$4.354. $$What is the correct mass to administer, rounded to the correct number of significant figures?

Accepted Answer

$$133 mg$$

Question 19

Which of the following best describes the correct order of operations and rounding for the calculation $$2.404 + 9.848 	imes 5.928 - 5.434$$?

Accepted Answer

Multiply first, then add and subtract, rounding at each step to the correct significant figures or decimal places.

Guided Practice: Significant Figures and Calculations in Chemistry

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