Question

The area of treasury box with length $1.6\times {10}^4$ and width $2.45\times {10}^3$ is $a\times {10}^b$. Find the value of $a$ and $b$.

• A. $a$ = 3.92 and $b$ = 6
• B. $a$ = 3.92 and $b$ = 7
• C. $a$ = 2.92 and $b$ = 6
• D. $a$ = 2.92 and $b$ = 7

Answer 1

The correct option is B $a$ = 3.92 and $b$ = 7

$\text{Given}$:
$\text{Length of the box}=1.6\times {10}^4$
$\text{Width of the box}=2.45\times {10}^3$
$\text{Area of the box}=\text{Length}\times \text{Width}$
$=(1.6\times {10}^4)\times (2.45\times {10}^3)$
$=(1.6\times 2.45)\times ({10}^4\times {10}^3)$
$=3.92\times \left({10}^{4+3}\right)$
$=3.92\times {10}^7$

On comparing the above expression with $a\times {10}^b$, we get,
$a$ = 3.92 and $b$ = 7