What is the Definition of an Equivalent Decimal

Equivalent Decimals

Decimals are a type of fractional number. The decimal 0.2 represents the fraction \(\frac{2}{10}\). We know \(\frac{2}{10}\) is equivalent to \(\frac{1}{5}\), since \(\frac{1}{5}\) times of \(\frac{2}{2}\) is \(\frac{2}{10}\).
Therefore, the decimal 0.2 is equivalent to \(\frac{1}{5}\) or \(\frac{2}{10}\) or \(\frac{20}{100}\) or \(\frac{200}{1000}\) etc.

Observe the following diagrammatic representation:
What is the Definition of an Equivalent Decimal 1

All these three decimals i.e., 0.2, 0.20, and 0.200, have the same value and so they are called equivalent decimals.
Example 1: Give next two decimal numbers in the sequence:
(a) 1.32, 1.42, 1.52, …, …
(b) 1.14,1.25, 1.36, …, …
Solution:
(a) 1.32,1.42,1.52,1.62,1.72
(b) 1.14,1.25,1.36,1.47,1.58

Writing or removing zeros at the end of the decimal does not change its value.
Examples
0. 5 =0.50 = 0.500
= 0.5000 = 0.50000
6.2 = 6.20 = 6.200
= 6.2000 = 6.2000

Example 2: Write the number name for 207.652.
Solution: 207.652 = Two hundred seven point six five two

Example 3: Write the decimal fraction 35.439 in expanded form.
Solution:
What is the Definition of an Equivalent Decimal 3