Question

the depth of a lake is 15.8 m.
a. jada accurately measured the depth of the lake to the nearest meter. what measurement did jada get?
b. by how many meters does the measured depth differ from the actual depth?
c. express the measurement error as a percentage of the actual depth. round to the nearest hundredth percent.

Explanation:

Step1: Round 15.8 to nearest meter

To round 15.8 to the nearest meter, we look at the decimal part. Since \(0.8 \geq 0.5\), we round up the whole number part. So \(15.8\) rounded to the nearest meter is \(16\).

Step2: Find the difference (part b)

The actual depth is \(15.8\) m and the measured depth is \(16\) m. The difference is \(16 - 15.8 = 0.2\) m.

Step3: Calculate percentage error (part c)

The formula for percentage error is \(\frac{\text{Error}}{\text{Actual Value}} \times 100\%\). Here, error is \(0.2\) m and actual value is \(15.8\) m. So \(\frac{0.2}{15.8} \times 100\% \approx 1.27\%\) (rounded to nearest hundredth percent).

Answer:

a. \(16\)
b. \(0.2\)
c. \(1.27\)