Question

Write the following decimal number in the expanded form:
i. 2.034.

Answer 1

Hint: The given decimal number is to be expanded by multiplying the 1st term with one, the second term is divided by 10, the 3rd term divided by 100, and the fourth term is divided by 1000. The numbers after the division and multiplication will be added to each other and the decimal sign will be removed. Since the number has only four digits we go till thousands number notions.

Complete step-by-step answer:
We will multiply the first term with one
1st digit: \[2\to 2\times 1\]
 The term towards the right side of the decimal side will have a division with 10,100 and 1000 respectively since they are in the tenth hundredth and thousand places after the first digit.
2nd digit(1st digit from right side of the decimal):
\[\to 0\times \dfrac{1}{10}\]
3rd digit:
\[\to 3\times \dfrac{1}{100}\]
4th digit:
\[\to 4\times \dfrac{1}{1000}\]
Now, we will add all the multiplied and divided terms:
\[\left( 2\times 1 \right)+\left( 0\times \dfrac{1}{10} \right)+\left( 3\times \dfrac{1}{100} \right)+\left( 4\times \dfrac{1}{1000} \right)\]
Thus, the expanded form of the number 2.304 is given as \[\left( 2\times 1 \right)+\left( 0\times \dfrac{1}{10} \right)+\left( 3\times \dfrac{1}{100} \right)+\left( 4\times \dfrac{1}{1000} \right)\].

Note: The terms left and right of the decimal point will have a different function. From the left of the decimal point, we will multiply each digit starting with 1, 10, 100, and so on. From the first digit towards the right of the decimal point, we will start dividing the digits with 10,100 and so on.
Take note that from the left of the decimal point we start the multiplication from 1, 10, and so on but from the right side of the decimal we start dividing with 10, 100, and so on.