Decimal fractions are numbers that have a whole number part and a fractional part separated by a decimal point. When decimal fractions are unlike fraction however they are equal in value are called equivalent fractions.

**For example:**

1.1, 1.10, 1.1000

All are equivalent fraction as the actual value is 1.1 or 11/10

In decimal fractions in the fractional part zeros at the end does not have any value until and unless there is any number after the zero.

Here are few examples and state whether they are equivalent fractions or not. State the reasons for your answer.

**(i)** 4.001, 45, 45.01, 45.10

These are not equivalent decimal fractions as:

4.001 = 4001/1000

45

45.01 = 4501/100

45.10 = 4510/100

Here we can see that all the fractions have different values hence they cannot be termed as equivalent fractions.

**(ii)** 23.23, 23.230, 23.2300

These are equivalent decimal fractions as:

23.23 = 2323/100

23.230 = 23230/1000

23.2300 = 232300/10000

The value of all the fractions are 2323/100 hence these decimal numbers are equivalent fractions

**(iii)** 45.40, 45.400, 45.4000

These are equivalent decimal fractions as:

45.40 = 4540/100

45.400 = 45400/1000

45.4000 = 454000/10000

The value of all the fractions are 4540/100 hence these decimal numbers are equivalent fractions

**(iv)** 54, 54.20, 54.23, 5474

These are not equivalent decimal fractions as:

54

54.20 = 5420100

54.23 = 5423/100

5474

Here we can see that all the fractions have different values hence they cannot be termed as equivalent fractions.

**(v)** 2.01, 2.0101, 2.0100,
2.015

These are not equivalent decimal fractions as:

2.01 = 201/100

2.0101 = 20101/10000

2.0100 = 20100/10000

2.015 = 2015/1000

Here we can see that all the fractions have different values hence they cannot be termed as equivalent fractions.

**(vi)** 5.23, 5.230, 5.230000,
5.23000

These are equivalent decimal fractions as:

5.23 = 523/100

5.230 = 5.230/1000

5.230000 = 5230000/1000000

5.23000= 523000/100000

The value of all the fractions is 523/100 hence these decimal numbers are equivalent fractions

**(vii)** 52.00, 52.002, 52.03,
52.01, 52.06, 52.68

These are not equivalent decimal fractions as:

52.00 = 52/100

52.002 = 52002/1000

52.03 = 5203/100

52.01 = 5201/100

52.06 = 5206/100

52.68 = 5268/100

**(viii)** 95.56, 95.560,
95.5600, 95.56000

These are equivalent decimal fractions as:

95.56 = 9556/100

95.560 = 95560/1000

95.5600 = 955600/10000

95.56000 = 9556000/10000

The value of all the fractions is 9556/100 hence these decimal numbers are equivalent fractions

**(ix)** 45.632, 45.321, 45.001,
45.007, 452.01

These are not equivalent decimal fractions as:

45.632 = 45632/1000

45.321 = 45321/1000

45.001 = 45001/1000

45.007 = 45007/1000

452.01 = 45201/100

**(x)** 69.23, 69.230, 69.2300, 69.230000

These are equivalent decimal fractions as:

69.23 = 6923/100

69.230 = 69230/1000

69.2300 = 692300/10000

69.230000 = 69230000/1000000

The value of all the fractions is 6923/100 hence these decimal numbers are equivalent fractions.

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