Significant Figures Math Example 2

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

Example 2

medium
A rectangle measures 4.54.5 cm by 3.253.25 cm. Calculate the area to the correct number of significant figures.

Solution

  1. 1
    Compute: 4.5×3.25=14.6254.5 \times 3.25 = 14.625 cm2^2.
  2. 2
    4.54.5 has 22 significant figures; 3.253.25 has 33 significant figures.
  3. 3
    For multiplication, use the fewer significant figures: 22.
  4. 4
    Round 14.62514.625 to 22 significant figures: 1515 cm2^2.

Answer

Area =15= 15 cm2^2 (22 significant figures).
Reporting 14.62514.625 cm2^2 implies false precision since one measurement has only 22 significant figures. The rule for multiplication — limit to the fewest sig figs — prevents reporting more certainty than the data supports.

About Significant Figures

Significant figures are the meaningful digits in a measured quantity, reflecting its precision.

Learn more about Significant Figures →

More Significant Figures Examples

Example 1 easy

Count the significant figures in each number: (a) [formula], (b) [formula], (c) [formula].

Example 3 easy

Round each to [formula] significant figures: (a) [formula], (b) [formula], (c) [formula].

Example 4 medium

A chemist measures [formula] mL of solution using a burette and [formula] mL using a dropper. She ad

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