Significant Figures and Scientific Notation

How many significant figures are in the number 0.004560?

• 2

• 3

• 4

• 5

Answer explanation

The number 0.004560 has four significant figures: the digits 4, 5, 6, and the trailing zero after the decimal point is significant. Leading zeros are not counted, but all non-zero digits and trailing zeros in a decimal are.

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DOK Level 1: Recall

Identify the number of significant figures in 123.45.

• 3

• 4

• 5

• 6

Answer explanation

The number 123.45 has five significant figures: 1, 2, 3, 4, and 5. All non-zero digits are significant, and the digits after the decimal point are also counted. Therefore, the correct answer is 5.

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DOK Level 1: Recall

Round the number 0.006789 to three significant figures.

• 0.0067

• 0.00679

• 0.0068

• 0.007

Answer explanation

To round 0.006789 to three significant figures, we focus on the first three non-zero digits: 678. The next digit (9) rounds the last significant figure (7) up, resulting in 0.00679.

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DOK Level 1: Recall

Round 4567.89 to two significant figures.

• 4500

• 4600

• 4570

• 4568

Answer explanation

To round 4567.89 to two significant figures, we look at the first two digits (45). The next digit (6) rounds the 5 up, resulting in 4600. Thus, the correct answer is 4600.

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DOK Level 1: Recall

What is the scientific notation for 0.000345?

Answer explanation

To convert 0.000345 to scientific notation, move the decimal point 4 places to the right, giving 3.45. Thus, it is expressed as 3.45 × 10^{-4}, making the correct choice 3.45 × 10^{-4}.

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DOK Level 1: Recall

Express 7,890,000 in scientific notation.

Answer explanation

To express 7,890,000 in scientific notation, we write it as 7.89 multiplied by 10 raised to the power of 6, since the decimal is moved 6 places to the left. Thus, the correct answer is 7.89 \times 10^6.

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DOK Level 1: Recall

• 567

• 5670

• 56700

• 0.567

Answer explanation

To convert 5.67 × 10^3 to standard notation, move the decimal point 3 places to the right, resulting in 5670. Thus, the correct answer is 5670.

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DOK Level 1: Recall

Convert 0.00089 to scientific notation.

Answer explanation

To convert 0.00089 to scientific notation, move the decimal point 4 places to the right, giving 8.9. Thus, it becomes 8.9 x 10^{-4}, which is the correct choice.

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DOK Level 1: Recall

Answer explanation

To multiply, first multiply the coefficients: 3.2 × 4.5 = 14.4. Then, add the exponents: 10^2 × 10^3 = 10^(2+3) = 10^5. Combine to get 14.4 × 10^5. Adjusting for significant figures (2 sig figs), the answer is 1.4 × 10^6.

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DOK Level 2: Skill/Concept

Answer explanation

To divide, calculate \( \frac{6.0 \times 10^5}{2.0 \times 10^2} = 3.0 \times 10^{5-2} = 3.0 \times 10^3 \). The result has 2 significant figures, matching the least precise number (2.0). Thus, the answer is \( 3.0 \times 10^3 \).

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DOK Level 2: Skill/Concept