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Quizzes > High School Quizzes > Science

Practice Quiz: Sig Fig Multiplication & Division

Enhance accuracy and confidence through engaging exercises

Difficulty: Moderate
Grade: Grade 10
Study OutcomesCheat Sheet
Colorful paper art promoting Sig Fig Showdown, a quiz for high school science and math students.

Easy
When multiplying 2.5 by 3.42, how many significant figures should the final result have?
5
3
2
4
The rule for multiplication is that the result should have the same number of significant figures as the factor with the fewest significant figures. Since 2.5 has 2 significant figures and 3.42 has 3, the final result should have 2 significant figures.
In division, the final answer should have as many significant figures as which number in the calculation?
The average significant figures of the numbers
It is arbitrarily determined
The number with the fewest significant figures
The number with the most significant figures
For both multiplication and division, the final result is determined by the factor with the least number of significant figures. This rule ensures that the result reflects the precision of the least precise measurement.
When dividing 6.0 by 2.00, what is the correct answer rounded to the appropriate significant figures?
3
3.0
3.00
3.000
The numerator has 2 significant figures and the denominator has 3, so the final answer must be rounded to 2 significant figures. Therefore, 3.0 is the correctly rounded value.
Which of the following numbers is expressed with exactly three significant figures?
5.0
0.050
5.06
5.600
The number 5.06 is written with three significant figures: 5, 0, and 6. The other options either have fewer or more significant figures based on standard rules.
When multiplying 4.0 by 3.456, to what number of significant figures should the product be rounded?
3
5
4
2
The final product must have as many significant figures as the factor with the fewest, which in this case is 4.0 with 2 significant figures. Therefore, the product should be rounded to 2 significant figures.
Medium
Calculate (7.85 - 1.2) ÷ 3.45 and round the result to the appropriate number of significant figures.
2.8
2.70
2.73
2.7
Since the factor 1.2 has only 2 significant figures, the final result of the calculation must be rounded to 2 significant figures. The computed value rounds to 2.7, satisfying the significant figure rules.
Multiply 0.00456 by 789. What is the product rounded to three significant figures?
3.60
0.00360
3.6
3.598
Both factors have three significant figures, so the product must be rounded to 3 significant figures. Multiplying gives roughly 3.598, which rounds to 3.60 when limited to 3 significant figures.
Divide (8.40 - 10^3) by 2.1 and round the result to the proper number of significant figures.
4 - 10^3
4000
4.00 - 10^3
4.0 - 10^3
The factor 2.1 has the fewest significant figures (2), so the final result must be rounded to 2 significant figures. Expressing 4000 as 4.0 - 10^3 meets this requirement.
When multiplying numbers in scientific notation, how do you determine the number of significant figures in the final answer?
It is the sum of the significant figures of the individual numbers
It is the same as the number in the calculation with the fewest significant figures
It is based on the exponents of 10
It is determined by the number of digits in the result
When performing multiplication with numbers in scientific notation, only the significant figures in the coefficients are considered. The final answer should have as many significant figures as the factor with the fewest significant figures.
Calculate (12.3 - 10^-2) - (4.56 - 10^3) and round the answer to the correct number of significant figures.
5.60 - 10^2
5.61 - 10^2
5.62 - 10^2
5.61 - 10^3
Both numbers have 3 significant figures, so the final answer must also be rounded to 3 significant figures. The multiplication yields about 560.88, which rounds to 5.61 - 10^2.
How many significant figures are in the number 0.00078?
2
4
3
1
Leading zeros are not significant. In 0.00078, only the digits 7 and 8 are significant, so the number has 2 significant figures.
Divide 9.99 by 3.0. What is the correctly rounded result based on significant figure rules?
3.30
3.0
3.33
3.3
Since 9.99 has 3 significant figures and 3.0 has 2, the final result must be rounded to 2 significant figures. Dividing yields approximately 3.33, which rounds to 3.3.
Multiply 0.12 by 0.034. What is the product rounded to the correct number of significant figures?
0.004
0.0040
0.00408
0.0041
Each factor has 2 significant figures, so the product must be rounded to 2 significant figures. The unrounded product is 0.00408, which rounds to 0.0041.
What does the term 'significant figures' refer to in a numerical measurement?
The digits that contribute to the precision of the measurement, including all certain digits and the first uncertain digit
The digits after the decimal point only
All digits in the number regardless of their size
Only the non-zero digits in the measurement
Significant figures include all the digits in a measurement that are reliable, plus the first uncertain digit. This concept reflects the precision of the measurement.
When multiplying 0.0045 by 3.20, to how many significant figures should the product be rounded?
3 significant figures
4 significant figures
5 significant figures
2 significant figures
The product must have as many significant figures as the factor with the fewest, which is 0.0045 with 2 significant figures. Therefore, the final result should be rounded to 2 significant figures.
Hard
Evaluate (3.456 ÷ 1.2) - 2.00 and provide the answer rounded to the proper number of significant figures.
5.8
5.76
5.80
6
Although the intermediate calculation gives 5.76, the limiting factor is 1.2, which has only 2 significant figures. Thus, the final answer must be rounded to 2 significant figures, yielding 5.8.
Calculate (7.891 - 10^-3) - (5.4 - 10^2) ÷ (2.00 - 10^-1) and round your answer to the correct number of significant figures.
21
2.13 - 10^1
2.1 - 10^1
21.3
The number 5.4 has only 2 significant figures, which limits the overall precision. The calculated value is approximately 21.31, which when rounded to 2 significant figures is best expressed as 2.1 - 10^1.
Multiply 0.075 by 0.0048 and express the answer in scientific notation with the correct significant figures.
3.60 - 10^-4
3.6 - 10^-4
3.6 - 10^-3
36 - 10^-4
Both 0.075 and 0.0048 have 2 significant figures, so their product must also be presented with 2 significant figures. Multiplying yields 0.00036, which is written as 3.6 - 10^-4 in scientific notation.
Divide 0.00648 by 0.12. What is the result and how many significant figures does it contain?
0.054 (2 significant figures)
0.0054 (2 significant figures)
0.054 (3 significant figures)
0.0648 (3 significant figures)
0.00648 has 3 significant figures while 0.12 has 2. The calculation must be rounded to the lesser count, giving 0.054 which contains 2 significant figures.
Evaluate (5.400 ÷ 1.20) - 3.0 and express your answer with the correct number of significant figures.
14
1.35 - 10^1
13.5
14.0
Dividing 5.400 by 1.20 gives 4.5, and multiplying by 3.0 yields 13.5. However, because 3.0 has only 2 significant figures, the final answer must be rounded to 2 significant figures, resulting in 14.
0
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Study Outcomes

  1. Analyze numerical values to identify proper significant figures in multiplication and division.
  2. Apply rules of significant figures to solve exam-style practice problems.
  3. Evaluate measurement precision by maintaining correct significant figure usage.
  4. Calculate outcomes with appropriate significant figures in multi-step calculations.
  5. Enhance test readiness through consistent application of significant figure principles.

Sig Fig Multiplication & Division Cheat Sheet

  1. Match sig figs in multiplication and division - In multiplication and division, your result should carry the same number of significant figures as the measurement with the fewest. For example, 3.16 (3 sig figs) × 0.307 (3 sig figs) × 5.7 (2 sig figs) is rounded to 2 sig figs. Pearson: Significant Figures in Calculations
  2. Practice spotting significant figures - Get comfortable identifying which digits count. For instance, in 0.0030681 the first three zeros are just placeholders, so there are five significant figures (3, 0, 6, 8, 1). CliffsNotes: Identifying Significant Figures
  3. Remember trapped zeros are significant - Any zero between non-zero digits always counts. In 5.029, all four digits are significant because that zero sits right between the 5 and 2. CliffsNotes: Middle Zeros Rule
  4. Ignore leading zeros - Zeros at the start of a number just mark the decimal place and aren't significant. So 0.0030681 still has only five significant figures. CliffsNotes: Leading Zeros Rule
  5. Round only the final answer - Keep all your extra digits during calculations to avoid rounding errors, then round off only your final result to the correct sig figs. This trick helps you stay precise and accurate! Chemistry Steps: Rounding Tips
  6. Apply rules step by step in multistep problems - For mixed operations, do multiplication/division first (apply sig fig rules), then addition/subtraction (apply decimal place rules). It's like following a recipe in the right order! Chemistry Steps: Multistep Calculations
  7. Use scientific notation for clarity - Express very big or tiny numbers in scientific notation to show exactly how many sig figs you mean. For example, 0.00045 becomes 4.5 × 10❻❴ (2 sig figs). RMIT Learning Lab: Scientific Notation
  8. Tackle practice problems - The more you practice, the more natural sig figs become. Try multiplying 35.6 by 42: since 35.6 has 3 sig figs and 42 has 2, your answer should have 2 sig figs. Scientific Tutor: Practice Problems
  9. Count exact numbers as infinite sig figs - Exact counts (like 5 apples) or defined quantities (1 dozen) don't limit precision. They're considered to have an infinite number of significant figures. BYJU's: Exact Numbers in Sig Figs
  10. Stay consistent for reliable results - Use sig fig rules consistently in every step of your calculations. Consistency is your cheat code for accuracy and precision in chemistry! RMIT Learning Lab: Consistency in Significant Figures
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