Class 11 >> Physics >> physical-world-and-measurement >> accuracy-errors-and-significant-figures >> count-significant-figures-in-a-number
Skip to Practice

count-significant-figures-in-a-number

🚀 Counting significant figures in a number is essential in scientific measurements as it reflects the precision of the measurement. Significant figures are the digits in a number that contribute to its accuracy. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding how to count significant figures helps in reporting measurements accurately and avoiding misleading precision.

Theory Explanation

Identifying Non-Zero Digits

All non-zero digits (1-9) are always significant. For example, in the number 123.45, all five digits are significant.

Counting Zeros

Leading zeros (zeros before the first non-zero digit) are not significant. For example, in 0.0045, only the digits 4 and 5 are significant, giving us 2 significant figures. Zeros between non-zero digits are significant. For example, in 1002, all four digits are significant. Trailing zeros in a decimal number are significant. For example, in 2.300, there are four significant figures.

Trailing Zeros in Whole Numbers

Trailing zeros in whole numbers without a decimal point are ambiguous. For example, in 1500, it is unclear how many significant figures there are unless specified (e.g., 1500. has four significant figures).

Key Points

  • 🎯 Non-zero digits are always significant.
  • 🎯 Leading zeros are not significant.
  • 🎯 Zeros between significant digits are significant.
  • 🎯 Trailing zeros in decimal numbers are significant.
  • 🎯 Trailing zeros in whole numbers are ambiguous without a decimal point.

🛠 Simulation is being generated. Please check back in a few moments.

Examples:💡

Count the significant figures in the number 0.00456.

Solution:

Step 1: Identify the non-zero digits: 4, 5, and 6 are significant.

Step 2: Leading zeros (0.00) are not significant, so we only count 4, 5, and 6.

Step 3: Total significant figures = 3.

Common Mistakes

  • Mistake: Students often count leading zeros as significant figures.

    Correction: Remember that leading zeros are not counted as significant figures.

  • Mistake: Confusing trailing zeros in whole numbers with significant figures.

    Correction: Clarify whether the number has a decimal point to determine if trailing zeros are significant.

← Back Start Practice