The density of a substance is measured as $3.42 \times 10^{-2}$ kg/m$^3$. How many significant figures are in this measurement?

## CORE INFORMATION\n✓ **Answer**: [Option C]\n## CONCEPT FRAMEWORK\n\t**Primary Concept**: Significant Figures\n\t**Related Topics**: Measurement, Scientific Notation\n\t**Prerequisites**: Rules for identifying significant figures\n## SOLUTION PATHWAY\n**Given Information**:\n\t* Measured density: $3.42 \times 10^{-2}$ kg/m³\n**Method & Steps**:\n\t1. Identify the significant figures in the coefficient:\n\t\tReasoning: In scientific notation, all digits in the coefficient (the number before the power of 10) are considered significant.\n\t\tFormula/Rule: Rules for significant figures in scientific notation.\n\t2. Count the significant figures in the coefficient:\n\t\tWorking: The coefficient is 3.42, which has three digits.\n\t\tKey Point: The power of 10 (10^-2) does not affect the number of significant figures.\n\t3. Determine the total significant figures:\n\t\tResult: The number of significant figures in the measurement is 3.\n\t\tVerification: The number of significant digits are the number of digits in the mantissa.\n ## OPTION ANALYSIS\n[A] :x: [Incorrect. There are more than one significant figures.]\n[B] :x: [Incorrect. There are three significant figures, not two.]\n[C] ✓: [Correct. The number 3.42 has three significant digits. The exponent does not affect the number of significant figures.]\n[D] :x: [Incorrect. There are not four significant figures.]\n ## LEARNING AIDS\n\t**Common Mistakes**:\n\t\t1.[Error 1]: Counting the exponent as a significant figure. [Always remember that the exponent in scientific notation only indicates the magnitude and not the precision of the measurement.]\n\t\t2.[Error 2]: Not recognizing the rules for scientific notation. [Make sure you know the rules for significant figures in different formats.]\n\t**Quick Tips**:\n\t\t1.[Helpful shortcut]: The number of significant figures is equal to the number of digits in the coefficient of scientific notation.]\n\t\t2.[Memory aid]: Remember that leading zeros are not significant, but trailing zeros after a decimal point are significant. In scientific notation, all the digits in the coefficient are significant.

The measurement $4.00 \times 10^3$ m has how many significant figures?

## CORE INFORMATION\n✓ **Answer**: [Option C]\n## CONCEPT FRAMEWORK\n\t**Primary Concept**: Significant Figures\n\t**Related Topics**: Scientific Notation, Measurement\n\t**Prerequisites**: Understanding of significant figure rules\n## SOLUTION PATHWAY\n**Given Information**:\n\t\tMeasurement: $4.00 \times 10^3$ m\n\t\t\n**Method & Steps**:\n\t1.\tIdentify the non-zero digits: The non-zero digit is 4.\n\t\tReasoning: All non-zero digits are significant.\n\t\tFormula/Rule: N/A\n\t2.\tIdentify zeros between non-zero digits: There are no zeros between non-zero digits.\n\t\tWorking: N/A\n\t\tKey Point: N/A\n\t3.\tIdentify trailing zeros after a decimal point: There are two trailing zeros after the decimal point.\n\t\tReasoning: Trailing zeros after a decimal are significant.\n\t\tFormula/Rule: N/A\n\t4.\tCount the significant figures: Count all significant digits.\n\t\tResult: 3 significant figures\n\t\tVerification: 4.00 has 3 significant figures.\n ## OPTION ANALYSIS\n[A] :x: Incorrect. There are three significant figures, not one.\n[B] :x: Incorrect. There are three significant figures, not two.\n[C] ✓: Correct. The number 4.00 has three significant figures because the zeros after the decimal point are significant.\n[D] :x: Incorrect. There are three significant figures, not four.\n ## LEARNING AIDS\n\t**Common Mistakes**:\n\t\t1.[Error 1]: Forgetting that trailing zeros after a decimal point are significant. [How to avoid]: Always check the decimal point and trailing zeros.\n\t\t2.[Error 2]: Considering the power of 10 as a significant figure. [How to avoid]: The exponent part in scientific notation is not used to determine significant figures.\n\t**Quick Tips**:\n\t\t1.[Helpful shortcut]: Focus on the digits in the coefficient of the scientific notation, ignore the power of 10 when counting significant figures.\n\t\t2.[Memory aid]: Remember the rules for non-zero digits, zeros between non-zero digits, and trailing zeros after a decimal point.

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