Measures and accuracy：練習問題

Which of the following is the upper bound for a weight measured as \(4.8 \text{ kg}\) to the nearest \(0.1 \text{ kg}\)?

A rectangular plot of land has a length of \(15.4 \text{ m}\) and a width of \(8.2 \text{ m}\), both measured to the nearest \(10 \text{ cm}\).
What is the lower bound of the area of the plot?

A car travels \(120 \text{ miles}\) to the nearest \(10 \text{ miles}\). The time taken is \(2 \text{ hours}\) to the nearest hour.
What is the maximum possible average speed of the car?

A number \(x\) is rounded to \(2\) significant figures. The result is \(340\).
Complete the error interval for \(x\).

Estimate the value of \(\frac{41.3 \times 19.8}{0.49}\) by rounding each number to \(1\) significant figure.

Use inequality notation to specify the error interval for a length, \(L\), that has been rounded to \(70 \text{ cm}\) to the nearest \(10 \text{ cm}\).

The side length of a square is measured as \(4.5 \text{ cm}\) correct to 1 decimal place.
Calculate the lower bound for the area of the square.

A mass is given as \(5.4 \text{ kg}\) correct to the nearest \(0.1 \text{ kg}\).
Write down the upper bound of this mass.

A piece of timber is \( 2.5 \text{ metres} \) long, measured to the nearest \( 10 \text{ cm} \).

(a) Convert \( 2.5 \text{ m} \) into centimetres.
(b) Find the lower bound and the upper bound of the length in centimetres.
(c) If the timber is cut into \( 50 \text{ cm} \) lengths (measured exactly), what is the maximum number of full lengths that could definitely be guaranteed?

The length of a piece of string is measured as \( 18.4 \text{ cm} \) to the nearest millimetre.

(a) Write down the lower bound and the upper bound for the length of the string using inequality notation.
(b) If three of these identical strings are joined together, what is the maximum possible total length?