Question

YOU BE THE TEACHER
Your friend adds $2.5\times {10}^9$ and $5.3\times {10}^8$. Is your friend correct? Explain your reasoning.

Answer 1

Yes answer given by my friend is correct, because when we add the given numbers we get

$2.5\times {10}^9+$$5.3\times {10}^8$

$={10}^8\times (2.5\times 10+5.3)$ (taking ${10}^8$ as common factor)

$={10}^8\times (25+5.3)$ (solving multiplication and then adding digits in brackets)

$={10}^8\times (30.3)$

$={10}^8\times (3.03\times {10}^1)$

$=3.03\times {10}^{1+8}$ (using exponent law ${\mathrm{a}}^{\mathrm{m}}\times {\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}+\mathrm{n}}$)

$=3.03\times {10}^9$

So, Yes answer given by my friend is correct.