Rational numbers are any numbers that may be written as a fraction. In different phrases, you may rewrite the quantity so it’ll have a numerator and a denominator.
a
b
during which a and b are integers and b not equal to zero.
Discover that we mentioned b can’t be zero. It’s as a result of any quantity divided by 0 has no reply.
Examples of rational numbers
Now, why are 2 and 0 rational numbers as effectively?
It’s as a result of 2 and 0 could be written as
x could be any quantity since 0 divided by any quantity is zero. Discover although that in keeping with the definition x can’t be zero!
Decimal growth of rational numbers
We are able to additionally write rational numbers as decimals.
We do that by performing a fast division. We divide the numerator by the denominator.
As an example,
Discover you can proceed division to maintain getting zeros for the decimal locations after 4.
You may also write 0.400000000000 as 0.40̄
The bar on high of 0 implies that if we proceed to carry out lengthy division, we’ll hold getting an infinite variety of zeros.
2
5
right into a decimal is to note that we are able to multiply 5 by 20 and a pair of by 20
Dividing by 100 or another energy of 10 is a simple course of.
In case you are dividing by 10, simply transfer the decimal level one place to the left.
In case you are dividing by 100, simply transfer the decimal level 2 locations to the left.
and so forth…
40
100
, the decimal level is after 0 for 40.
Transferring that two locations to the left deliver the decimal level proper earlier than the 4.
A rational quantity can have both repeating decimal growth or terminating decimal growth.
Repeating decimal growth:
A decimal growth during which the numbers repeat in precisely the identical order.
For instance, 0.251251251251 is a repeating decimal growth as a result of 251 retains repeating in the identical order.
Terminating decimal growth:
A decimal growth that ends in all zeros.
For instance, 0.150 is a terminating decimal growth.
Here’s a determine summarizing rational numbers or the “various kinds of rational numbers”
 Pure numbers are rational numbers since any pure quantity could be written within the type a/b. For instance, 2 could be written as 2/1.
 Complete numbers are rational numbers since any complete quantity could be written within the type a/b. For instance, 9 could be written as 9/1.
 Integers are rational numbers since any integer could be written within the type a/b. For instance, 8 could be written as 8/1.
 Nonterminating decimal numbers with repeating patterns are rational numbers. For instance, 0.2121212121 is a rational quantity since it may be written as 7/33.
 Terminating decimal numbers are rational numbers. For instance, 0.75 is a rational quantity since it may be written as 3/4.
 Easy fractions whose numerators and denominators are complete numbers are rational numbers. For instance, the fraction 2/5 is a rational quantity. Nevertheless, the fraction 1.3/5 is just not a rational quantity since 1.3 is just not an integer in keeping with the definition of a rational quantity.
Rational numbers FAQs

No. 0.6666666 is a rational quantity. Nevertheless, it isn’t an integer. Some rational numbers are integers. For instance, 8/1, 5/1 are rational numbers and integers as effectively since 8/1 = 8 and 5/1 = 5. Nonetheless, each integer is a rational quantity!

Sure, rational numbers are actual numbers since actual numbers embrace all units of numbers besides complicated numbers.

No, not essentially!There are damaging rational numbers and optimistic rational numbers akin to 1/2, 15/6, 4/3, 6/20.

3.14 is a wellknown irrational quantity often called pi. 3.14 has an infinite variety of digits after the decimal level that don’t have repeating patterns. Due to this fact, pi can’t be written as a ratio or be a rational quantity.

As a rule of thumb, if the quantity has a bunch of various digits after the decimal level with no particular sample, the quantity is just not rational.
Check your understanding of this lesson with the rational numbers quiz beneath.