Question

How to write 3.141 in expanded notation?

Answer 1

Hint: To write the expanded notation for 3.141. We have to write each digit is written as a product of the digit and the place value that it occupies. So, therefore in that form, we will write the expanded notion.

Complete step by step answer:
To write $$3.141$$ in expanded notation.
Let us start expanding from right to left.
The 1 which is in the thousandth's place will be converted by $${\displaystyle \frac{1}{1000}}$$and added by the remaining part as shown below.
$$3.141$$
$$\Rightarrow 3.14+{\displaystyle \frac{1}{1000}}$$
Now, the 4 which is in hundredth’s place will be converted by $${\displaystyle \frac{1}{100}}$$and added by the remaining part as shown below.
$$\Rightarrow 3.1+{\displaystyle \frac{1}{100}}+{\displaystyle \frac{1}{1000}}$$
Now, the 1 which is in ten’s place will be converted by $${\displaystyle \frac{1}{10}}$$and added by the remaining part as shown below.
$$\Rightarrow 3+{\displaystyle \frac{1}{10}}+{\displaystyle \frac{1}{100}}+{\displaystyle \frac{1}{1000}}$$
Now, the 3 which is in one’s place will be converted by$$3\times 1$$ and it will become the base of the expansion.
$$\Rightarrow 3\times 1+{\displaystyle \frac{1}{10}}+{\displaystyle \frac{1}{100}}+{\displaystyle \frac{1}{1000}}$$
So, therefore the expansion for 3.141 is $$3\times 1+{\displaystyle \frac{1}{10}}+{\displaystyle \frac{1}{100}}+{\displaystyle \frac{1}{1000}}$$.

Note:
Students should be aware of decimal and place notation concepts. Because the lack of concept may cause many types of errors. Examiners may give an expanded form and ask to convert it into decimal form. So students should practice this type of problem too.