Question

How do you write the decimal $8.823$ in expanded form?

Answer 1

Hint: Here, we are required to write the given decimal number in its expanded form. Thus, we will use the place value system and multiply the digits with their place values and add them together to find the required expanded form of the given decimal number.

Complete step by step solution:
In order to write the given decimal number in expanded form, we should know that:
The expanded form notation for the decimal numbers is the mathematical expression to show the sum of the values of each digit in that number. To write the expanded form of any number, we use the place value system.
The place value refers to the value of a digit in a number. The value for each number is based on the position of number.
Therefore, in the decimal number, $8.823$
We have 8 ones, i.e. $8 \times 1 = 8$
After the decimal point, we have
8 ones of tenth: $8 \times \dfrac{1}{{10}} = \dfrac{8}{{10}}$
2 ones of hundredth: $2 \times \dfrac{1}{{100}} = \dfrac{2}{{100}}$
3 ones of thousandth: $3 \times \dfrac{1}{{1000}} = \dfrac{3}{{1000}}$
Therefore, the expanded form of the given decimal number $8.823$ is:
 $8.823 = 8 + \dfrac{8}{{10}} + \dfrac{2}{{100}} + \dfrac{3}{{1000}}$
 In other words, we can write the fractions in decimal form as:
$8.823 = 8 + 0.8 + 0.02 + 0.003$

Therefore, the decimal $8.823$in expanded form is written as: $8 + \dfrac{8}{{10}} + \dfrac{2}{{100}} + \dfrac{3}{{1000}}$or $8 + 0.8 + 0.02 + 0.003$
Thus, this is the required answer.

Note:
In mathematics, a decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. The dot in a decimal number is called a decimal point. The digits following the decimal point show a value smaller than one. The concept of expanded form is useful in comprehending the value of a number as well as the numeric value of a quantity.