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Number - Significant Figures

Grade 8IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Significant figures are the digits in a number that contribute to its precision. They include all non-zero digits, zeros between non-zero digits, and trailing zeros in a decimal number.

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Rule 1: All non-zero digits are significant. For example, 123.45123.45 has 55 significant figures.

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Rule 2: Zeros between non-zero digits (sandwich zeros) are significant. For example, 40054005 has 44 significant figures.

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Rule 3: Leading zeros (zeros at the beginning) are NOT significant. They are just placeholders. For example, 0.00450.0045 has 22 significant figures.

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Rule 4: Trailing zeros in a decimal number are significant. For example, 4.5004.500 has 44 significant figures.

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Rule 5: Trailing zeros in a whole number without a decimal point are usually NOT significant unless specified. For example, 500500 is generally considered to have 11 significant figure.

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When rounding to nn significant figures, identify the nthn^{th} digit. If the digit following it is 55 or more, round up the nthn^{th} digit. If it is less than 55, leave the nthn^{th} digit as it is.

📐Formulae

If digit (n+1)≥5  ⟹  Round up digit n\text{If digit } (n+1) \geq 5 \implies \text{Round up digit } n

If digit (n+1)<5  ⟹  Keep digit n unchanged\text{If digit } (n+1) < 5 \implies \text{Keep digit } n \text{ unchanged}

💡Examples

Problem 1:

Round 0.0056720.005672 to 22 significant figures.

Solution:

0.00570.0057

Explanation:

The leading zeros are not significant. The first significant figure is 55 and the second is 66. The third digit is 77. Since 7≥57 \geq 5, we round the second digit (66) up to 77.

Problem 2:

Round 84,51284,512 to 33 significant figures.

Solution:

84,50084,500

Explanation:

The first three significant figures are 8,4,8, 4, and 55. The fourth digit is 11. Since 1<51 < 5, the 55 remains unchanged. We replace the remaining digits with zeros to maintain the place value.

Problem 3:

How many significant figures are in the number 4.020×1034.020 \times 10^3?

Solution:

44 significant figures

Explanation:

In scientific notation, all digits in the coefficient are significant. The digits are 4,0,2,4, 0, 2, and 00. The trailing zero after the decimal is significant.

Problem 4:

Calculate 12.5×2.012.5 \times 2.0 and give the answer to the correct number of significant figures.

Solution:

2525

Explanation:

When multiplying, the result should have the same number of significant figures as the measurement with the fewest significant figures. 12.512.5 has 33 sf and 2.02.0 has 22 sf. 12.5×2.0=25.012.5 \times 2.0 = 25.0. Rounding 25.025.0 to 22 sf gives 2525.