Question

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

Answer 1

Do you mean change `8.1 xx 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.

Answer 2

`color(red)0 xx 1 + color(red)0 xx 1/10 + color(red)0 xx 1/100 + color(red)0 xx 1/100 + color(red)8 xx 1/1000 + color(red)1 xx 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 = color(red)4 xx 1000 + color(red)0 xx 100 + color(red)2 xx 10 + color(red)5 xx 1`

Note

`4025 -> "Standard Notation"`

`4 xx 1000 + 0 xx 100 + 2 xx 10 + 5 xx 1 -> "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 `1/10 = "One - Tenth"`

`0.00425 = color(red)0 xx 0 + color(red)0 xx 1/10 + color(red)0 xx 1/100 + color(red)4 xx 1/1000 + color(red)2 xx 1/(10,000) + color(red)5 xx 1/(100,000)`

Now;

How do you convert `8.1 xx 10^-4` into expanded notation

First we should convert it to standard notation;

`8.1 xx 10^-4 = 0.00081 -> "Standard Notation"`

Now converting to Expanded Notation;

`0.00081 = color(red)0 xx 1 + color(red)0 xx 1/10 + color(red)0 xx 1/100 + color(red)0 xx 1/100 + color(red)8 xx 1/1000 + color(red)1 xx 1/(10,000)`