Question

exercise 2
with a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. with micrometer calipers, you measure the width of the rectangle to be 5.98 mm. use the correct number of significant figures: what are (a) the area of the rectangle; (b) the ratio of the rectangle’s width to its length; (c) the perimeter of the rectangle; (d) the difference between the length and the width; and (e) the ratio of the length to the width?

Explanation:

Step1: Define length and width

Let length $l = 12$ mm and width $w=5.98$ mm.

Step2: Calculate area (a)

Area $A=l\times w$. Since $l$ has 2 significant - figures, the result should have 2 significant - figures. $A = 12\times5.98=71.76\approx72$ mm².

Step3: Calculate width - to - length ratio (b)

$\frac{w}{l}=\frac{5.98}{12}\approx0.4983\approx0.50$ (2 significant - figures).

Step4: Calculate perimeter (c)

Perimeter $P = 2(l + w)=2(12 + 5.98)=2\times17.98 = 35.96\approx36$ mm (2 significant - figures).

Step5: Calculate length - width difference (d)

$l - w=12-5.98 = 6.02\approx6.0$ mm (2 significant - figures).

Step6: Calculate length - to - width ratio (e)

$\frac{l}{w}=\frac{12}{5.98}\approx2.007\approx2.0$ (2 significant - figures).

Answer:

(a) 72 mm²
(b) 0.50
(c) 36 mm
(d) 6.0 mm
(e) 2.0