Question

A box contains $5\times {10}^2$ paper clips. Each paper clip weighs $7\times {10}^{-4}$ kilograms. What is the total weight of paper clips in the box?

Answer 1

Hint: Mass is used to measure the weight of an object. In the metric system of measurement, the most common units of mass are the gram and kilogram.
1 kilogram = 1000 grams
To solve this question we have to multiply the weight of one paper clip and the total number of paper clips in order to find the total weight of the box. And as the number and weight of paper clip are given in power form therefore we will convert them into the simplest form to solve the question easily. Hence we will convert the kilogram into gram to get the simplest term.

Complete step-by-step answer:
Given that:
Number of paper clips in a box = $5\times {10}^2$
Weight of one paper clip = $7\times {10}^{-4}kg$
To find the weight of one paper clip in gram, we have to multiply it by 1000.
As, 1kilogram = 1000 grams
$$\begin{gathered} \therefore 7\times {10}^{-4}kg=7\times {10}^{-4}\times 1000 \\ =7\times {10}^{-4}\times {10}^3 \\ =7\times {10}^{-4+3} \\ =7\times {10}^{-1} \\ =0.7gram \end{gathered}$$
Total weight of paper clips in the box = (Number of paper clips in a box)*(Weight of one paper clip)
Let the total weight be W.
$$\begin{gathered} W=\left(5\times {10}^2\right)\times \left(0.7\right) \\ W=3.5\times {10}^2 \\ W=350grams \end{gathered}$$
Therefore, the total weight of paper clips in the box = 350 grams
Note: The quantity of matter in an object is called its mass. We must know that the meaning of mass of a body is different from that of the weight of that body. The two terms, mass and weight, are different in the real sense. Weight of an object changes from place to place, above and below the surface of the earth, but the mass of a body never changes.