# Equivalent Decimal Fractions

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

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

(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

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

(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.

## You might like these

• ### Word Problems on H.C.F. and L.C.M. | Highest Common Factor | Lowest Co

We have already learnt H.C.F, L.C.M and the relationship between the two and now we will learn on how to do word problems on H.C.F. and L.C.M. Note: In word problems on H.C.F. and L.C.M we have to remember two points: • When we are asked to find out maximum, highest

• ### Worksheet on H.C.F. and L.C.M. | HCF × LCM = 1st Number × 2nd Number

This topic will provide worksheet to students on H.C.F and L.C.M which will help to judge themselves their level of understanding of the topic and the areas where they need more careful study and analysis. This worksheet will serve as a yardstick for measuring the level of

• ### Relationship between H.C.F. and L.C.M. |HCF× LCM=1st Number×2nd Number

This topic discusses about the relationship between H.C.F and L.C.M in case of two numbers. The relationship between H.C.F and L.C. M of two number states that: H.C.F × L.C.M = First number × Second number Hence from this relationship we can find the following: H.C.F

• ### Examples to Find Least Common Multiple of Three Numbers by using Divis

This topic would provide examples on how to find least common multiple of three numbers. Various examples on finding L.C.M would help the learners in understanding the topic better. Here are few examples illustrated on finding the least common multiple of three numbers using

• ### To Find Lowest Common Multiple by using Division Method | Examples

This topic discusses about finding the lowest common multiple using division method. Steps to find the loqest common multiple using the division method: Step 1: Write the numbers in a row separating by commas Step 2: Then divide the given numbers (if possible both the

• ### Examples to Find Least Common Multiple of Two Numbers |Division Method

This topic would provide examples to find least common factor by using division method. This topic will help learners to clear their doubts and improve their understanding and knowledge on how to find out least common multiple (L.C.M) by division method.

• ### Examples to find Least Common Multiple by using Prime Factorization

This topic would provide various examples on finding the least common multiple using the method of prime factorization. Here are few examples illustrated on finding the least common multiple using the prime factorization method. 1. Find the least common multiple (L.C.M) of

• ### To Find Least Common Multiple by using Prime Factorization Method

This topic would discuss about how to find the least common multiple by using prime factorization method. Steps to find out the least common multiple by using prime factorization method: •First find all the prime factors of the given number .Then write all the prime factors

• ### Least Common Multiple (L.C.M.) | Lowest Common Multiple | Examples

In the last topic we have discussed about common multiples that is same multiples of two or more numbers. Now here we will discuss about the least common multiple that is the smallest common multiple of two or more numbers. Here are few examples illustrated on least common

• ### Common Multiples | What is Common Multiples? | Three Common Multiples

This topic would deal with common multiples. If some of the multiples of two or more number are same then those same multiples are termed as common multiples. Here are few examples illustrating common multiples: List the two common multiples of 5 and 6

• ### Multiples | Important Facts about Multiple | Even and Odd Multiples

This topic would deal with multiples. Multiples of a number are actually the tables of a certain number. If we are talking about multiple of 2 then it is actually the tables of 2. When we have learnt table we have learnt the tables till 10 or 12 that is till 2 multiplied

• ### Highest Common Factor of Three Numbers by using Division Method

This topic would discuss about finding highest common factor using the division method. We have already learnt finding the highest common factor by prime factorization method but it is not suitable when we are dealing with large numbers. Division method is quite convenient

• ### Find Highest Common Factor of Two Numbers by using Division Method

We have already learnt the method of finding highest common factor using division method. Here are few more examples given to clear your understanding, concepts and improve your knowledge on how to find H.C.F. this topic would provide a wide range of examples will help the

• ### To Find Highest Common Factor by using Division Method | Examples

This topic would discuss about finding the highest common factor of three numbers using the division method. We have learnt in our last topic about finding the highest common factor of two numbers. While doing with three numbers first we will find the highest common factor