# (8xx10^-7)(2xx10^5)?

## scientific notation

Oct 23, 2017

The answer of this calculation is $1.6 \times {10}^{-} 1$

#### Explanation:

When multiplying numbers in scientific notation, first you multiply the whole numbers.

In this case, they are $8 \mathmr{and} 2$, which equals $16.$

Then for the exponents: when multiplying, you add the exponents. So that would be $- 7 + 5 = - 2$.

We have $16 \times {10}^{-} 2$.

But in scientific notation, there must be only ONE digit before the decimal point.

$16 \times {10}^{-} 2 = 1.6 \times {10}^{-} 1$

In decimal notation the answer is $0.16$

Oct 25, 2017

$= 16 \times {10}^{-} 2 = 1.6 \times {10}^{-} 1$

#### Explanation:

Multiplying in scientific notation can be compared to multiplying in algebra:

$3 {x}^{4} \times 5 {x}^{3}$ can also be written as:

$\textcolor{red}{3 \times 5} \times \textcolor{b l u e}{{x}^{4} \times {x}^{3}}$

= color(red)(15) xx color(blue)(x^(4+3)" "larr bases are both $x$, so add the indices

$= \textcolor{red}{15} \times \textcolor{b l u e}{{x}^{7}}$

In scientific notation you might have:

$3 \times {10}^{8} \times 4 \times {10}^{11}$

$= \textcolor{red}{3 \times 4} \times \textcolor{b l u e}{{10}^{8} \times {10}^{11}}$

$= \textcolor{red}{12} \times \textcolor{b l u e}{{10}^{19}}$

However in scientific notation, there must be one digit before the decimal point:

$\textcolor{red}{12} \times \textcolor{b l u e}{{10}^{19}} = \textcolor{red}{1.2} \times \textcolor{b l u e}{{10}^{20}}$

In this example we have:

$8 \times {10}^{-} 7 \times 2 \times {10}^{5}$

$= \textcolor{red}{8 \times 2} \times \textcolor{b l u e}{{10}^{-} 7 \times {10}^{5}}$

$= \textcolor{red}{16} \times \textcolor{b l u e}{{10}^{- 7 + 5}}$

$= \textcolor{red}{16} \times \textcolor{b l u e}{{10}^{-} 2}$

However in scientific notation, there must be one digit before the decimal point:

$= \textcolor{red}{16} \times \textcolor{b l u e}{{10}^{-} 2} = \textcolor{red}{1.6} \times \textcolor{b l u e}{{10}^{-} 1}$

It is usual to give an answer in the same format as the question.

In decimal format this answer would be $0.16$