How do you convert 8.1 x 10^-4 into expanded notation?

Jun 28, 2018

Do you mean change $8.1 \times {10}^{- 4}$ to a normal number?

0.00081 would be the answer. The decimal point moves 4 places because you have the number 4. It moves to the left because it is a negative 4.

Jun 28, 2018

$\textcolor{red}{0} \times 1 + \textcolor{red}{0} \times \frac{1}{10} + \textcolor{red}{0} \times \frac{1}{100} + \textcolor{red}{0} \times \frac{1}{100} + \textcolor{red}{8} \times \frac{1}{1000} + \textcolor{red}{1} \times \frac{1}{10 , 000}$

Explanation:

Expanded notation is like reducing or deducing a number expansively in the Hundreds Tens and Units format to match the given value.

For example;

Expanded notation of $4025$

$4025 = \textcolor{red}{4} \times 1000 + \textcolor{red}{0} \times 100 + \textcolor{red}{2} \times 10 + \textcolor{red}{5} \times 1$

Note

$4025 \to \text{Standard Notation}$

$4 \times 1000 + 0 \times 100 + 2 \times 10 + 5 \times 1 \to \text{Expanded Notation}$

Another example;

Expanded notation of $0.00425$

Now we know that when a number divided by;

$10$ is known as Tenth

$100$ is known as Hundredth

$1000$ is known as Thousandth

$10 , 000$ is known as Ten Thousandth

$100 , 000$ is known as Hundredth Thousandth

e.g $\frac{1}{10} = \text{One - Tenth}$

$0.00425 = \textcolor{red}{0} \times 0 + \textcolor{red}{0} \times \frac{1}{10} + \textcolor{red}{0} \times \frac{1}{100} + \textcolor{red}{4} \times \frac{1}{1000} + \textcolor{red}{2} \times \frac{1}{10 , 000} + \textcolor{red}{5} \times \frac{1}{100 , 000}$

Now;

How do you convert $8.1 \times {10}^{-} 4$ into expanded notation

First we should convert it to standard notation;

$8.1 \times {10}^{-} 4 = 0.00081 \to \text{Standard Notation}$

Now converting to Expanded Notation;

$0.00081 = \textcolor{red}{0} \times 1 + \textcolor{red}{0} \times \frac{1}{10} + \textcolor{red}{0} \times \frac{1}{100} + \textcolor{red}{0} \times \frac{1}{100} + \textcolor{red}{8} \times \frac{1}{1000} + \textcolor{red}{1} \times \frac{1}{10 , 000}$