Question

Choose the options which is equivalent to the following expression:
$\left[\right(4.2\times {10}^3)+(7.8\times {10}^4)-(12\times {10}^2\left)\right]\times 120,000$

• A. $9.816\times {10}^9$
• B. $98.16\times {10}^7$
• C. $9.816\times {10}^7$
• D. $98.16\times {10}^{11}$

Answer 1

The correct option is A $9.816\times {10}^9$

$\text{Given}$: $(4.2\times {10}^3)+(7.8\times {10}^4)-(12\times {10}^2)\times 120,000$

Convert it into scientific notation,
$\left[\right(4.2\times {10}^3)+(7.88\times {10}^4)-(12\times {10}^2\left)\right]\times 1.2\times {10}^5$

As per BODMAS rule,
$=\left[\right(4.2\times {10}^3)+(78.8\times {10}^3)-(12\times {10}^2\left)\right]\times (1.2\times {10}^5)$
$=\left[\right(4.2+78.8)\times {10}^3-(12\times {10}^2\left)\right]\times (1.2\times {10}^5)$
$=\left[\right(83\times {10}^3)-(12\times {10}^2\left)\right]\times (1.2\times {10}^5)$
$=\left[\right(830\times {10}^2)-(12\times {10}^2\left)\right]\times (1.2\times {10}^5)$
$=(830-12)\times {10}^2\times (1.2\times {10}^5)$
$=(818\times {10}^2)\times (1.2\times {10}^5)$
$=(818\times {10}^2)\times (1200\times {10}^2)$
$=818\times 1200\times {10}^{2+2}$
$=981600\times {10}^4$
$=9.816\times {10}^9$