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Quizzes > High School Quizzes > Science

Significant Digits Practice Quiz

Sharpen skills with a significant digits test

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art depicting a trivia quiz on significant digits for high school science students.

How many significant digits does the number 0.00540 have?
2
3
4
5
Leading zeros are not counted as significant. Only the digits 5, 4, and the trailing zero (after the decimal) are significant, giving a total of three significant digits.
How many significant digits are in 123.45?
4
5
6
7
All non-zero digits in 123.45 are significant. This gives a total of five significant digits.
Which rule applies when multiplying numbers with significant digits?
The product has as many decimal places as the factor with the most decimals.
The product has as many significant digits as the factor with the fewest significant digits.
The product always retains all significant digits from both factors.
Significant digits are not considered in multiplication.
When multiplying, the result is limited by the factor with the fewest significant digits. This ensures that the precision of the product reflects the least precise measurement.
How can the ambiguous significant digits of the number 1500 be clearly indicated as having only two significant digits?
By writing it as 1.50 × 10^3
By writing it as 1500.0
By writing it as 1.5 × 10^3
By leaving it as 1500
Scientific notation removes ambiguity in significant digits. Expressing 1500 as 1.5 × 10^3 clearly indicates that there are only two significant digits.
Which type of zero is always considered significant?
Leading zeros
Captive zeros
Trailing zeros in a whole number without a decimal point
Zeros added solely to position the decimal point
Captive zeros, which appear between non-zero digits, are always significant. This is a fundamental rule in determining the number of significant figures.
How many significant digits are in the number 0.004070?
3
4
5
6
After ignoring the leading zeros, the digits 4, 0, 7, and the trailing zero after the decimal are all significant. This adds up to four significant digits.
When adding numbers, how should the final answer be rounded according to significant digit rules?
Round to the same number of significant digits as the number with the fewest digits.
Round to the least number of decimal places among the numbers added.
Round to the most precise measurement in the set.
Do not round the result.
For addition and subtraction, the key rule is to round the answer to the least number of decimal places present among the numbers being added. This ensures consistency in precision.
What is 3.14159 rounded to three significant digits?
3.14
3.142
3.15
3.141
Rounding 3.14159 to three significant digits retains the first three digits (3, 1, and 4). The following digit (1) does not round the 4 up, so the correct rounded value is 3.14.
Why is scientific notation useful in expressing significant digits?
It makes numbers more confusing.
It unambiguously shows the significant digits in a number.
It increases the number of significant digits.
It disguises the true value of a measurement.
Scientific notation displays the significant digits clearly by presenting a coefficient that includes all measured digits. This eliminates any ambiguity, especially for very large or very small numbers.
How many significant digits does 50.00 have?
2
3
4
5
The presence of a decimal point confirms that the trailing zeros are significant. Thus, 50.00 has four significant digits: 5, 0, 0, and 0.
If you multiply 2.0 by 3.456, what is the correctly rounded product?
6.912
7.0
6.91
7.00
The number 2.0 has only 2 significant digits, which limits the precision of the product. Multiplying 2.0 by 3.456 produces 6.912, but it must be rounded to 2 significant digits, resulting in 7.0.
When subtracting 12.11 from 15.6, to which decimal place should the result be rounded?
Nearest whole number
Tenths place
Hundredths place
Thousandths place
In subtraction, the final answer is rounded to the least number of decimal places of any number in the operation. Since 15.6 has one decimal place, the result should be rounded to the tenths place.
Which statement is not consistent with the rules of significant digits?
Leading zeros are not significant.
Captive zeros are always significant.
Trailing zeros in a whole number without a decimal point are always significant.
Zeros used to indicate a decimal point are significant.
Trailing zeros in a whole number without an explicit decimal point can be ambiguous and are not automatically considered significant. Therefore, the statement claiming they are always significant is incorrect.
Which of the following measurements clearly indicates the precision of the instrument?
12 cm
12.3 cm
12.30 cm
12.300 cm
The measurement 12.30 cm shows that the reading is precise to the hundredths place, clearly indicating the instrument's level of precision. This explicit display of significant digits helps avoid ambiguity in data reporting.
How is 0.000567 correctly expressed in scientific notation?
5.67 × 10^-4
5.6 × 10^-4
0.567 × 10^-3
56.7 × 10^-5
Expressing 0.000567 in scientific notation requires moving the decimal so that the coefficient is between 1 and 10. The correct representation that maintains all three significant digits is 5.67 × 10^-4.
What is the correctly rounded quotient when dividing 0.00450 by 2.0?
0.0023
0.0022
0.00225
0.002
Division should yield a result with the same number of significant digits as the measurement with the fewest significant digits. Since 2.0 has 2 significant digits, the quotient 0.00450 ÷ 2.0 must be rounded to 2 significant digits, resulting in 0.0023.
Given a distance of 150.0 m and a time of 12.30 s, how many significant digits should the calculated speed have?
2
3
4
5
Both 150.0 m and 12.30 s are expressed with 4 significant digits. When calculating speed (distance divided by time), the result should be reported using the same number of significant digits as the least precise measurement, which in this case is 4.
How should the sum of 0.126, 0.7, and 0.0825 be reported considering significant digit rules?
0.91
0.9085
0.9
1.0
In addition, the result is rounded to the least number of decimal places from the numbers being added. Since 0.7 has only one decimal place, the sum must be rounded to the tenths place, yielding 0.9.
Which expression correctly represents the product of 4.56 (3 significant digits) and 0.078 (2 significant digits) in scientific notation?
3.6 × 10^-1
3.56 × 10^-1
3.5568 × 10^-1
0.36 × 10^-1
Multiplying 4.56 by 0.078 gives approximately 0.35568. However, the factor 0.078 limits the result to 2 significant digits, so the product must be rounded to 0.36, which is expressed in scientific notation as 3.6 × 10^-1.
A measurement changes from 0.0040 to 0.00405. How many significant digits does the new value represent?
2
3
4
5
The original reading, 0.0040, has 2 significant digits. The new measurement, 0.00405, includes the digits 4, 0, and 5, indicating 3 significant digits. This reflects an increase in the precision of the measurement.
0
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Study Outcomes

  1. Understand the rules for identifying significant digits in numerical values.
  2. Apply proper rounding techniques based on significant digit guidelines.
  3. Analyze measurement precision and its impact on scientific calculations.
  4. Evaluate numerical results to determine the appropriate number of significant digits.
  5. Synthesize significant digit concepts to solve real-world scientific problems.

Significant Digits Cheat Sheet

  1. All non-zero digits are significant. Every digit from 1 through 9 always counts, so in 123.45 you've got five significant figures. This rule helps you keep track of precision in every calculation. Pearson: Significant Figures
  2. Zeros between non-zero digits are significant. In a number like 1002, both zeros sandwiched between the 1 and 2 matter, giving you four significant figures. Remember that any zero "trapped" between other digits is a VIP. Pearson: Significant Figures
  3. Leading zeros are not significant. In 0.056, the zeros merely set the decimal place, so only 5 and 6 actually count. Think of those zeros as quiet placeholders waiting in the wings. Pearson: Significant Figures
  4. Trailing zeros in a decimal number are significant. A value like 78.00 boasts four significant figures because those zeros after the decimal point are rock stars. They lock in your measurement's exactness. Pearson: Significant Figures
  5. Trailing zeros in a whole number without a decimal point are ambiguous. In 1500, it's unclear if those zeros count unless you see a decimal or overbar. To clear up the mystery, consider using scientific notation. Pearson: Significant Figures
  6. Addition & subtraction rule: Your answer should have the same number of decimal places as the measurement with the fewest decimals. For example, 150.0 g + 0.507 g becomes 150.5 g - not 150.507 g. Purdue: Sig Figs Guide
  7. Multiplication & division rule: Match the number of significant figures in your result to the measurement with the fewest sig figs. If you multiply 4.56 (three sig figs) by 1.4 (two sig figs), your answer gets two sig figs. Purdue: Sig Figs Guide
  8. Exact numbers have infinite significant figures. Defined quantities like 1 m = 100 cm don't limit your digits - they're considered perfect. Use them freely without worrying about losing precision. Britannica: Significant Figures
  9. Rounding rules: If the digit to the right is less than 5, round down; if it's greater than 5, round up. For instance, 33.742 rounded to one decimal place is 33.7. This keeps your numbers neat! Britannica: Significant Figures
  10. Use scientific notation to show sig figs clearly. Writing 4.5 × 10³ makes it obvious you have two significant figures and avoids any zero drama. This trick is especially handy for huge or tiny numbers. Britannica: Significant Figures
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