Question

Find the product of (5.2 · 10^-6) and (8 · 10^3).

Answer 1

 

$\displaystyle\\(5.2\cdot10^{-6})\times(8\cdot10^3)=\\\\=\underbrace{5.2\times8}_{41.6}\times\underbrace{10^{-6}\times10^{3}}_{10^{-6+3}}=\\\\=41.6\times10^{-6+3}=\boxed{\bf41.6\times10^{-3}}\\\\\texttt{Correct answer:}~~\boxed{\bf C)}$

Answer 2

Answer: B) $4.16\cdot10^{-2}$

Step-by-step explanation:

The given product : $(5.2\cdot10^{-6})\cdot (8\cdot10^3)$

First open parenthesis :

$5.2\cdot10^{-6}\cdot 8\cdot10^3$

Write decimal values together and power of 10s together.

$5.2\cdot 8\cdot10^{-6}\cdot10^3$

Using Law of exponent : $a^m\cdot a^n= a^{m+n}$

The above expression becomes.

$41.6\cdot10^{-6+3}=41.6\times10^{-3}$

In scientific notation, the decimal must be placed after one digit (from left).

$41.6\times10^{-3}=4.16\times10\times10^{-3}\\\\=4.16\cdot10^{-3+1}\\\\=4.16\cdot10^{-2}$

Hence, the correct answer is B) $4.16\cdot10^{-2}$ .