Question

1. convert to scientific notation with the number of significant digits indicated. (a) 27 000 cm (3 sig dig) - (b) 370 000 g (2 sig dig) - (c) 0.000 0078 (1 sig dig) - (d) 23 789 m (1 sig dig) - (e) 0.058700 l (4 sig dig)

Explanation:

Step1: Recall scientific - notation form

Scientific notation is \(a\times10^{n}\), where \(1\leqslant|a|\lt10\) and \(n\) is an integer.

Step2: Convert 27000 cm to scientific - notation with 3 sig - dig

Move the decimal point 4 places to the left, \(a = 2.70\) (3 significant digits) and \(n=4\). So it is \(2.70\times 10^{4}\text{ cm}\).

Step3: Convert 370000 g to scientific - notation with 2 sig - dig

Move the decimal point 5 places to the left, \(a = 3.7\) and \(n = 5\). So it is \(3.7\times 10^{5}\text{ g}\).

Step4: Convert 0.0000078 to scientific - notation with 1 sig - dig

Move the decimal point 6 places to the right, \(a=8\times10^{- 7}\) (rounding 7.8 to 8 for 1 significant digit).

Step5: Convert 23789 m to scientific - notation with 1 sig - dig

Move the decimal point 4 places to the left, \(a = 2\times10^{4}\text{ m}\) (rounding 2.3789 to 2 for 1 significant digit).

Step6: Convert 0.058700 L to scientific - notation with 4 sig - dig

Move the decimal point 2 places to the right, \(a = 5.870\times10^{-2}\text{ L}\).

Answer:

(a) \(2.70\times 10^{4}\text{ cm}\)
(b) \(3.7\times 10^{5}\text{ g}\)
(c) \(8\times 10^{-7}\)
(d) \(2\times 10^{4}\text{ m}\)
(e) \(5.870\times 10^{-2}\text{ L}\)