# Standard form of rational number explained

Learn and know what is the meaning of the standard form of rational number? We know what is a rational number? But do you know what does the standard form of a rational number (Q) means?

The Standard form of a rational number or the simplest form of rational number, both these meanings are the same. Now I think you will get an idea about what is standard form of any rational number. I hope you know how to write in simplest form of any rational number. Simplest form means writing the given rational number in its lowest terms. If we take one rational number i.e. $\frac { 22 }{ 8 }$. We say $\frac { 22 }{ 8 }$ is not in simplest form because cancellation is possible here. With 2 table we can cancel 22 and 8. If we cancel with 2 table we get one new rational number i.e. $\frac { 11 }{ 4 }$. Now if we observe $\frac { 11 }{ 4 }$ there is no cancellation possible. So we can leave here $\frac { 11 }{ 4 }$ as it is. Now we say $\frac { 11 }{ 4 }$ is in simplest form. Now you have understood simplest form of a rational number. Almost the same meaning applies for standard form of a rational number also. We will see that now.

## Standard form of rational number meaning as follows:

We know that rational number will be of the form $\frac { a }{ b }$ where “a” and “b” are integers and b is not equal to zero. For example, $\frac { 22 }{ 7 }$, $\frac { 6 }{ 5 }$, $\frac { -9 }{ 45 }$, $\frac { 8 }{ 41 }$, $\frac { -47 }{ -56 }$, 3, -78 … are rational numbers. In these rational numbers, the rational numbers whose numerators and denominators H.C.F is equal to 1 are said to be in the standard form. So we can define that if the rational number $\frac { a }{ b }$ has no factors other than 1 then we say that rational number is in standard from.

$\frac { 22 }{ 7 }$ is said to be in standard form because the H.C.F of 22 and 7 is 1.

$\frac { 6 }{ 5 }$ is also said to be in standard form because the H.C.F of 6 and 5 is 1.

$\frac { -9 }{ 45 }$ is not in standard form because H.C.F of 9 and 45 is not equal to 1.

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