Rounding Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Round ฯ€โ‰ˆ3.14159265โ€ฆ\pi \approx 3.14159265\ldots to 44 significant figures. Then round 0.00384720.0038472 to 33 significant figures.

Solution

  1. 1
    Recall: significant figures are counted from the first non-zero digit; leading zeros do not count.
  2. 2
    For ฯ€\pi to 44 significant figures: the significant digits are 3,1,4,13, 1, 4, 1; the next digit is 55, so round up the last kept digit: 3.1423.142.
  3. 3
    For 0.00384720.0038472 to 33 significant figures: leading zeros are not significant. The significant digits are 3,8,43, 8, 4; the next digit is 7โ‰ฅ57 \geq 5, so round up the 44 to 55: 0.003850.00385.

Answer

ฯ€โ‰ˆ3.142\pi \approx 3.142; 0.0038472โ‰ˆ0.003850.0038472 \approx 0.00385
Significant figures count from the first non-zero digit. Leading zeros are never significant โ€” they just locate the decimal point. Rounding to significant figures rather than decimal places is more appropriate for measurements of varying magnitude.

About Rounding

Replacing a number with a nearby simpler approximation at a specified place value, using the digit to the right to decide.

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