Learn what is meant by an equivalent decimal fraction and also know about the rules and definition all in detail. Refer to the problems on equivalent decimal fractions and examples to know in-depth about equivalent decimal fractions in the article. Learn how to obtain the equivalent decimals for a given set of decimal numbers, determine whether a set of decimals are equivalent or not.
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Equivalent Decimal Fraction – Definition
It is defined as any two decimal fractions that are said to be an equivalent decimal fraction that is they represent the same value. It is also defined as they are unlike fractions that are equal in value.
Example: \(\frac { 2 }{ 10 } \) or 0.2 and \(\frac { 2}{ 100} \) or 0.02 are said to be equivalent decimal fractions. So, by keeping any number of zeros to the right of the decimal part does not change the value.
Examples:
1. 1.9, 1.90, 1.900, 1.9000
Above given decimals are equivalent decimals and all of the given them are equal to 1.9 or \(\frac { 19 }{ 10 } \)
2. 0.4, 0.40, 0.400, 0.4000
Above given decimals are equivalent decimals and all of the given them are equal to 0.4 or \(\frac { 4 }{ 10 } \)
3. 6.7, 6.70, 6.700, 6.7000
Above given decimals are equivalent decimals and all of the given them are equal to 6.7 or \(\frac { 67 }{ 10 } \)
4. 70.89, 70.890, 70.8900, 70.89000
Above given decimals are equivalent decimals and all of the given them are equal to 70.89 0r \(\frac { 7089 }{ 100 } \)
5. 44.78, 44.780, 44.7800, 44.7800
Above given decimals are equivalent decimals and all of the given them are equal to 44.78 0r \(\frac { 44.78 }{ 100 } \)
Note: By adding zeros to the extreme right to the decimal part of the decimal number will not change the value of the number.
Equivalent Decimal Fractions Examples
Example 1:
Prove that 0.5 and 0.50 are equivalent decimal fractions.
Solution:
Given decimals are 0.5 and 0.50
0.5 can be written as \(\frac { 5 }{ 10 } \)
0.50 can be written as \(\frac { 5 }{ 100 } \)
By solving \(\frac { 5}{ 10 } \) we get \(\frac { 1}{ 2 } \) and similarly for \(\frac { 5 }{ 100 } \) we get \(\frac { 1 }{ 2 } \).
So, both got the same value i.e \(\frac { 1 }{ 2 } \)
Therefore, 0.5 and 0.50 are equivalent decimal fractions.
Hence proved.
Example 2.
Check whether 4.4 and 4.04 are equivalent decimal fractions or not.
Solution:
Given decimals are 4.4 and 4.04
4.4 can be written as \(\frac { 44 }{ 10 } \)
4.04 can be written as \(\frac { 404}{ 100 } \)
By solving \(\frac { 44}{ 10 } \) we get \(\frac { 22}{ 5 } \) and similarly for \(\frac { 404 }{ 100 } \) we get \(\frac { 101}{ 25 } \).
So, both did not get the same value.
Therefore, 4.4 and 4.04 are not equivalent decimal fractions.
Example 3.
Prove that 1.8 and 1.80 are equivalent decimal fractions.
Solution:
Given decimals are 1.8 and 1.80
1.8 can be written as \(\frac { 18 }{ 10 } \)
1.80 can be written as \(\frac { 180}{ 100 } \)
By solving \(\frac { 18}{ 10 } \) we get \(\frac { 9}{ 5 } \) and similarly for \(\frac { 180 }{ 100 } \) we get \(\frac { 9 }{ 5 } \).
So, both got the same value i.e \(\frac { 9 }{ 5 } \)
Therefore, 1.8 and 1.80 are equivalent decimal fractions.
Hence proved.
Example 4.
Check whether 0.8 and 0.08 are equivalent decimal fractions or not.
Solution:
Given decimals are 0.8 and 0.08
0.8 can be written as \(\frac { 8 }{ 10 } \)
0.08 can be written as \(\frac { 8}{ 100 } \)
By solving \(\frac { 8}{ 10 } \) we get \(\frac { 4}{ 5 } \) and similarly for \(\frac { 8 }{ 100 } \) we get \(\frac { 4 }{ 50 } \).
So, both did not get the same value.
Therefore, 0.8 and 0.08 are not equivalent decimal fractions.