# How do you write 0.000 000 000 154 in scientific notation?

Mar 9, 2016

$0.000000000154 = 1.54 \cdot {10}^{-} 10$

#### Explanation:

$0.000000000154 = 1.54 \cdot {10}^{-} 10$[Ans]

Mar 9, 2016

In depth explanation of how to obtain$\text{ } 1.54 \times {10}^{- 10}$

#### Explanation:

We need to be able to convert this number so that it looks line 1.54 but in such a way that its actual value has not changed.

Consider the example of 32. This would will to look like 3.2

If we divide it by 10 we then have$\text{ } \frac{32}{10} = 3.2$

But this has changed its value so we need a slightly different approach.

$\textcolor{b l u e}{\text{Point 1}}$

$\textcolor{b r o w n}{\text{If we multiply a number by 1 we do not change its value}}$

$\textcolor{b l u e}{\text{Point 2}}$

$\textcolor{b r o w n}{\text{The value of 1 can be presented in many ways}}$
For this type of calculation we need it to be of format $\frac{n}{n}$ where $n$ is any number other than zero

$\textcolor{b l u e}{\text{Method}}$

The way to use this method for our example is to do this:

$32 \times \frac{10}{10}$

$\frac{32}{10} \times 10$

Divide the denominator of 10 into 32 giving

$3.2 \times 10$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Using this method to solve your question}}$

Given:$\text{ } 0.000000000154$

To achieve 1.54 we need to keep the decimal point where it is and slide the number towards the left for 10 digits.

To mathematically achieve this we have $0.000000000154 \times {10}^{10}$

But ${10}^{10}$ is not the value 1

So we need to multiply by ${10}^{10} / {10}^{10}$ giving

$0.000000000154 \times {10}^{10} \times \frac{1}{10} ^ 10$

Apply the process of $0.000000000154 \times {10}^{10}$ leaving

$1.54 \times \frac{1}{10} ^ 10$

But another way of writing $\frac{1}{10} ^ 10 \text{ is } {10}^{- 10}$ which means $\div {10}^{10}$

This gives: $1.54 \times {10}^{- 10}$