Answer

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**Hint:**To solve this question we need to know about fraction and decimal. We should also know the way of its expansion. The number given to us is in decimal form and we need to change to fractional form which will be added. We will write the number in such a manner that the number in front of decimal point will be as a natural number while that after decimal point will be written in form of fraction having the denominator in form of ${{10}^{n}}$ where n is the natural numbers.

**Complete step by step answer:**

The question asks us to expand the decimal number $0.294$ which will be in the form of sum of fraction. For doing this we will first analyse the number given to us which is $0.294$. So in this the number left to the decimal point is zero while that on the right side of the decimal point are $2,9$ and $4$ which are at tenth, hundredth and thousandth positions respectively. For the case of the number zero which is left to the decimal point is at one's place. On writing the above explanation mathematically we get:

$\Rightarrow 0.294$

The numbers after the decimal point will be written in fractional form as shown below:

$\Rightarrow 0+\dfrac{2}{10}+\dfrac{9}{100}+\dfrac{4}{1000}$

$\therefore $ The following decimal in expanded form: $0.294$ is $0+\dfrac{2}{10}+\dfrac{9}{100}+\dfrac{4}{1000}$.

**Note:**We can check whether the expanded form is correct or not by adding up all the fractions if the number we get is the same number as that given in the question. First we will convert the fraction into decimal form individually and then we will add all the decimal numbers. On doing this we get:

$\Rightarrow 0+\dfrac{2}{10}+\dfrac{9}{100}+\dfrac{4}{1000}$

Now changing the fraction into decimal we get:

$\Rightarrow 0+0.2+0.09+0.004$

On adding the whole term we get:

$\Rightarrow 0.294$

Since the number is the same as that of the question, the answer is correct.

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