Question

If the age of fossil is determined by the given expression $9,900,000,000+(4.5\times {10}^6-2.8\times {10}^5)\times 5\times {10}^4$, then it is equivalent to .

• A. $31\times {10}^{12}$
• B. $3.1\times {10}^{11}$
• C. $31\times {10}^{11}$
• D. $3.1\times {10}^{10}$

Answer 1

The correct option is B $3.1\times {10}^{11}$

Given: $9,900,000,000+(4.5\times {10}^6-2.8\times {10}^5)\times 5\times {10}^4$

Converting into scientific notation,

$=9.9\times {10}^{10}+(4.5\times {10}^6-2.8\times {10}^5)\times 5\times {10}^4$

$=9.9\times {10}^{10}+(45\times {10}^5-2.8\times {10}^5)\times 5\times {10}^4$

$=9.9\times {10}^{10}+(42.2\times {10}^5)\times (5\times {10}^4)$

$=9.9\times {10}^{10}+211\times {10}^{5+4}$

$=9.9\times {10}^{10}+211\times {10}^9$

$=9.9\times {10}^{10}+21.1\times {10}^{10}$

$=(9.9+21.1)\times {10}^{10}$

$=\left(31\right)\times {10}^{10}$

$=\left(3.1\right)\times {10}^{11}$