**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:

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:**

**Read More About:**

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- What is a Decimal Value and Place Value of Decimals?
- How do you Round to the Nearest Ten Thousand
- Converting To and From Scientific Notation
- What is the Difference between Ascending and Descending Order
- Addition and Subtraction of Decimals
- How do you Multiply and Divide Decimals?
- How do you Convert Fractions into Decimals and Vice Versa
- How do you Convert Unlike Decimals into Like Decimals