Approximate values & estimation：練習問題

Round off the number \(0.004092\) to 2 significant figures.

The measured speed of sound in air is recorded as \(343\) m/s, correct to 3 significant figures. Calculate the maximum possible percentage error associated with this measurement, expressing your answer correct to 3 significant figures.

A rectangular garden has a length of \(15.5\) meters and a width of \(8.2\) meters. Both measurements are given correct to one decimal place. A fence is to be built around the garden. What is the maximum possible length of the fence needed, correct to two decimal places?

Round the number \(0.05738\) to 3 significant figures.

The actual length of a rope is \(2.45 \text{ m}\). A student measures the length as \(2.5 \text{ m}\) (corrected to 1 decimal place). Find the percentage error in this measurement, correct to 2 significant figures.

Round the number \( 0.003064 \) to 2 significant figures.

Evaluate the expression \( \frac{15.9 \times 4.1}{1.98} \) by rounding each number to the nearest whole number.

A cylindrical tank has a base radius of \( 2.0 \text{ m} \) and a height of \( 5.0 \text{ m} \), both correct to the nearest \( 0.1 \text{ m} \). Calculate the maximum absolute error in the calculated volume of the tank. (Take \( \pi = 3.14 \))

A student uses a ruler to measure the dimensions of a small rectangular block of wood. The measured values are as follows:
Length = \( 12.4 \text{ cm} \)
Width = \( 8.6 \text{ cm} \)
The measurements are recorded correct to the nearest \( 0.1 \text{ cm} \).

(a) Find the maximum absolute error of the measurements.
(b) Find the upper limit and lower limit of the actual area of the wooden block. (Give your answers correct to 2 decimal places.)
(c) Calculate the percentage error of the area calculation, using the measured values as the base. (Give your answer correct to 3 significant figures.)

A laboratory technician measures the volume of a chemical solution as \( 245 \text{ mL} \), correct to the nearest \( 5 \text{ mL} \).

(a) Find the maximum absolute error and the relative error of this measurement.

(b) State the range of the actual volume, \( V \), of the solution.

(c) If the actual volume is exactly \( 243.2 \text{ mL} \), calculate the percentage error of the measurement. (Give your answer correct to 2 decimal places.)