Question

How do you write 519.148 in expanded exponential form ?

Answer 1

Hint: Expanded Notation can be defined as a way of expressing numbers by showing the value of each digit. Writing a number in expanded notation is not the same as writing in expanded form. In expanded notation, a number is represented as the summation of each digit multiplied by its place whereas in expanded form, addition is only used between places' value number.

Complete step-by-step solution:
There would be better understanding after this example.
Let us take a random number. Maybe $1547$. Let us write this number in expanded form as well as in expanded notation.
Number when it is written in expanded form is as follows :
$\Rightarrow 1547=1000+500+40+7$
Now let us write it in expanded notation.
Number when it is written in expanded exponential form is as follows :
$\Rightarrow 1547=1\times 1000+5\times 100+4\times 10+7\times 1.$
You can even enclose each term within parenthesis.
The original form of the number i.e $1547$ is called as the standard form.
To expand a particular number from its standard form, we need to expand it into the sum of each digit multiplied by its matching place value which are ones, tens, hundreds, and so on.
Now, let us write the given number in expanded exponential form.
It is as follows :
$\Rightarrow 519.148=(5\times 100)+(1\times 10)+(9\times 1)+\left({\displaystyle \frac{1}{10}}\right)+\left({\displaystyle \frac{4}{100}}\right)+\left({\displaystyle \frac{8}{1000}}\right)$ .
$\therefore$ Hence, the expanded exponential form of $519.148$is $(5\times 100)+(1\times 10)+(9\times 1)+\left({\displaystyle \frac{1}{10}}\right)+\left({\displaystyle \frac{4}{100}}\right)+\left({\displaystyle \frac{8}{1000}}\right)$.

Note: We should be careful while writing a number in expanded exponential forms as there is a lot of scope for confusion after the decimal point. The number of zeroes which are to be allocated to each number after decimal might seem like a problem. But with practice, we will not be confused anymore. We should not have any confusion between expanded form and expanded exponential form.