# How do you write 0.386 in scientific notation?

Jun 9, 2016

In scientific notation $0.386 = 3.86 \times {10}^{- 1}$

#### Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of $10$.

Note that moving decimal $p$ digits to right is equivalent to multiplying by ${10}^{p}$ and moving decimal $q$ digits to left is equivalent to dividing by ${10}^{q}$.

Hence, we should either divide the number by ${10}^{p}$ i.e. multiply by ${10}^{- p}$ (if moving decimal to right) or multiply the number by ${10}^{q}$ (if moving decimal to left).

In other words, it is written as $a \times {10}^{n}$, where $1 \le a < 10$ and $n$ is an integer.

To write $0 , 386$ in scientific notation, we will have to move the decimal point one point to right, which literally means multiplying by $10$.

Hence in scientific notation $0.386 = 3.86 \times {10}^{- 1}$ (note that as we have moved decimal one point to right we are multiplying by ${10}^{- 1}$.

Jun 9, 2016

$3.86 \times {10}^{- 1}$

#### Explanation:

Given:$\text{ } 0.386$

$\textcolor{b l u e}{\text{Point 1}}$
Objective is to have just one none zero digit to the left of the decimal and everything else on the other side.

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$\textcolor{b l u e}{\text{Point 2}}$
If you multiply a value by 1 you do not change its 'intrinsic' value. However, 1 comes in many forms. For example:

$\text{ "2/2"; "4/4"; "sqrt(7)/sqrt(7)"; "(-1)/(-1)"; } \frac{10}{10}$

So we can multiply by 1 and not change the intrinsic value but we can change the way it looks.
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$\textcolor{b l u e}{\text{Answering your question}}$

Multiply by 1 but in the form of $1 = \frac{10}{10}$ giving:

$0.386 \times \frac{10}{10}$

This is the same as: $\left(0.386 \times 10\right) \times \frac{1}{10}$

Which is the same as: $\left(3.86\right) \times \frac{1}{10} \text{ "larr" nearly there!}$

Another way of writing $\times \frac{1}{10} \text{ is } \times {10}^{- 1}$

So $3.86 \times \frac{1}{10} \text{ "->" } 3.86 \times {10}^{- 1}$

So $0.386 \text{ is the same as } 3.86 \times {10}^{- 1}$