Math / Numbers & Operations

QuestionOne grain of this sand approximately weighs $7 \times 10^{-5} \mathrm{~g}$ . b) How many grains of sand are there in 6300 kg of sand? Give your answer in standard from.

Studdy Solution

STEP 1

1. The weight of one grain of sand is $7 \times 10^{-5}$ grams.
2. We need to find the number of grains in $6300$ kilograms of sand.
3. Conversion from kilograms to grams is necessary since the weight of a grain is given in grams.

STEP 2

1. Convert kilograms to grams.
2. Set up the equation to find the number of grains.
3. Solve the equation and express the answer in standard form.

STEP 3

Convert the mass of sand from kilograms to grams.
Since $1$ kilogram equals $1000$ grams, we have:
$6300 \, \text{kg} = 6300 \times 1000 \, \text{g}$
$6300 \, \text{kg} = 6.3 \times 10^6 \, \text{g}$

STEP 4

Set up the equation to find the number of grains of sand.
Let $n$ be the number of grains of sand. Then:
$n = \frac{\text{total mass of sand in grams}}{\text{mass of one grain of sand in grams}}$
$n = \frac{6.3 \times 10^6 \, \text{g}}{7 \times 10^{-5} \, \text{g}}$

STEP 5

Solve the equation to find $n$ .
$n = \frac{6.3 \times 10^6}{7 \times 10^{-5}}$
$n = \frac{6.3}{7} \times 10^{6 - (-5)}$
$n = 0.9 \times 10^{11}$
Convert to standard form:
$n = 9 \times 10^{10}$
The number of grains of sand in $6300$ kg of sand is:
$\boxed{9 \times 10^{10} \text{ grains}}$

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