Question

the mass of a grain of sand is about 10 to the power of negative three grams. about how many grains of sand are in the bag of sand?

Answer 1

We are given : The mass of a grain of sand = $10^{-3} grams.$

Bag contains = 10 kilograms of sand.

Let us concert 10 kg into grams first.

1 kg = 1000 grams.

10 kg = 10 × 1000 = 10000 grams = 10^4.

Therefore, bag contains 10^4 grams of sand.

Therefore, number of grains of sand are in the bag of sand of 10^4 grams =

The mass of a grain of sand in grams ÷ The mass of a grain of sand.

$\frac{10^4}{10^{-3}}$

=$10^{4-(-3)}$

=$10^{4+3}$

$=10^7 \ grains \ of \ sand.$

Therefore, $10^7$ grains of sand are in the bag of 10kg sand.