Question

Micaela measures her floor and records

its width as 3.2 m and its length as
3.8 m. She rounds her measurements
to the nearest meter and estimates that
the floor space in her room is 12 square
meters. What is the percent error of her
estimate? Round your answer to the
nearest tenth of a percent.

Answer 1

To calculate the percent error of Micaela's estimate, we use the original measurements to find the exact area, compare it to the estimated area, and apply the percent error formula, resulting in a percent error of 1.3% when rounded to the nearest tenth.

Step-by-step explanation:

The student rounded her measurements of her floor space to the nearest meter, getting an estimated area of 12 square meters.

To determine the percent error of her estimate, we first need to calculate the exact area using the original measurements: 3.2 m × 3.8 m = 12.16 m².

The percent error is given by the formula: (|Estimated Value - Exact Value| / Exact Value) × 100%.

Plugging in our values, we get (|12.0 m² - 12.16 m²| / 12.16 m²) × 100% = (0.16 m² / 12.16 m²) × 100% which approximately equals 1.3%.

Therefore, the percent error of Micaela's estimate rounded to the nearest tenth of a percent is 1.3%.