Question

The population of city A is $4.81\times {10}^6$ while the population of city B is $1.9\times {10}^5$ . What is their combined population (in millions)?

Answer 1

Detailed step-by-step solution:
The population of city $A=4.81\times {10}^6$
The population of city $B=1.9\times {10}^5$
Their combined population $=4.81\times {10}^6+1.9\times {10}^5$
$=4.81\times {10}^1\times {10}^5+1.9\times {10}^5$ (rewriting ${10}^6$ as ${10}^1\times {10}^5)$
$=48.1\times {10}^5+1.9\times {10}^5$ (rewriting $4.81\times {10}^1=48.1)$
$=(48.1+1.9)\times {10}^5$ (using distributive property)
$=50\times {10}^5$
$=5\times {10}^1\times {10}^5$ (rewriting $50$ as $5\times {10}^1$)
$=5\times {10}^6$ (using product of powers property, i.e., $a^m\times a^n=a^{m-n}$)
$=5$ million $(1$ million $={10}^6$)
$\Rightarrow$ Option A is correct.