Estimation, Units of Measurement and Accuracy：练习题

Convert the number 0.000000072 into standard form.

Find the value of \( P \) in standard form if \( P = \frac{a^2 - b}{c} \), given \( a = 5.0 \times 10^3 \), \( b = 4.0 \times 10^6 \), and \( c = 2.0 \times 10^{-2} \).

Evaluate the expression \( \sqrt[3]{2.7 \times 10^{-11} \times 10^6} \) and express the result in standard form.

Convert \(3.04 \times 10^{-4}\) into an ordinary number.

Calculate \( (3 \times 10^4)^2 \) and express the answer in standard form.

Round the number 0.099972 to 3 significant figures.

A cube has a volume of \( 2.7 \times 10^{-5} \text{ m}^3 \). Find the length of one edge of the cube in meters, expressing the result in standard form.

The speed of light is approximately \(3.00 \times 10^8\) m/s. Calculate the distance light travels in 1 hour, expressing the answer in standard form to 3 significant figures.

Consider the number \( N = 0.00045982 \).
(a) Round \( N \) to 3 significant figures.
(b) Express the result from part (a) in standard form.
(c) If the original number \( N \) is multiplied by \( 10^5 \), write the resulting number in standard form.

A rectangular park has a length of \( L = 4.2 \times 10^3 \) meters and a width of \( W = 2.5 \times 10^2 \) meters.
(a) Calculate the perimeter of the park in meters, expressing your answer in standard form.
(b) Calculate the area of the park in square meters, expressing your answer in standard form.
(c) If a worker can mow \( 5.0 \times 10^3 \) square meters of grass per hour, calculate the total time needed to mow the entire park.