Question

The weight of a stone is $45700000000000$ grams. What is the weight of the stone in standard form in kilograms?

• A. $4.57\times {10}^{11}$
• B. $0.457\times {10}^{11}$
• C. $4.57\times {10}^{10}$
• D. $45.7\times {10}^9$

Answer 1

The correct option is C $4.57\times {10}^{10}$

$45700000000000$ grams $=4.57\times {10}^{13}$ grams
$1$ kilogram $=1000$ grams $={10}^3$ grams
So, $1$ gram $={10}^{-3}$ kilogram
In order to express the weight of the stone in kilograms, we can write,
$4.57\times {10}^{13}$ grams $=4.57\times {10}^{13}\times 1$ gram
$=4.57\times {10}^{13}\times {10}^{-3}$ kilograms
$=4.57\times {10}^{13+(-3)}$ kilograms
$[$Since, ${\text{a}}^{\text{m}}\times {\text{a}}^{\text{n}}={\text{a}}^{\text{m+n}}$, for a non-zero integer $\text{a}]$
$=4.57\times {10}^{10}$ kilograms

Therefore, the weight of the stone in standard form in kilograms is $4.57\times {10}^{10}$ kilograms.