Math Problem Statement

State the number of significant figures in the following quantities a. 3.00100 g b. 0.0200 s c. 0.0023°C d. 0.0000055 g e. 1.6402 g f. 3.40 x 103 mL g. 1.020 L

Solution

Let's evaluate the number of significant figures for each quantity:

a. 3.00100 g

  • All non-zero digits and zeros between non-zero digits are significant. Trailing zeros after a decimal point are also significant.
  • Significant Figures: 6

b. 0.0200 s

  • Leading zeros are not significant, but trailing zeros after a decimal point are.
  • Significant Figures: 3

c. 0.0023°C

  • Leading zeros are not significant.
  • Significant Figures: 2

d. 0.0000055 g

  • Leading zeros are not significant.
  • Significant Figures: 2

e. 1.6402 g

  • All non-zero digits are significant.
  • Significant Figures: 5

f. 3.40 x 10³ mL

  • In scientific notation, the digits in the coefficient (3.40) are significant. The exponent doesn't affect the count of significant figures.
  • Significant Figures: 3

g. 1.020 L

  • Trailing zeros after a decimal point are significant.
  • Significant Figures: 4

Summary of Significant Figures:

  • a. 6
  • b. 3
  • c. 2
  • d. 2
  • e. 5
  • f. 3
  • g. 4

Would you like a detailed explanation on any of these?

Further related questions:

  1. How do leading and trailing zeros affect significant figures?
  2. What are the rules for significant figures in multiplication and division?
  3. How does scientific notation influence the count of significant figures?
  4. Can you give examples of quantities with exactly 1 significant figure?
  5. What is the difference between precision and accuracy in measurements?

Tip: Always use significant figures rules when performing calculations to maintain the correct level of precision.

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Math Problem Analysis

Mathematical Concepts

Significant Figures
Scientific Notation
Measurement Precision

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12