Rational Numbers
Rational numbers are any numbers that can be written as a fraction. In other words, you can rewrite the number so it will have a numerator and a denominator.
They have the form
a
/
b
in which a and b are integers and b not equal to zero.
Notice that we said b cannot be zero. It is because any number divided by 0 has no answer
Examples of numbers that are rational are:
Now, why are 2 and 0 examples of such numbers?
It is because 2 and 0 can be written as
x can be any number since 0 divided by any number is zero
Decimal expansion:
We can also write rational numbers as a decimals.
We do this by performing a quick division that is dividing the numerator by the denominator
For instance,
or
Notice that you can continue division to keep getting zeros for the decimal places after 4
The bar on top of 0 means that if we continue to perform long division, we will keep getting an infinite number of zeros.
Another way to convert
2
/
5
into a decimal is to notice that we can multiply 5 by 20 and 2 by 20
Diving by 100 or any other power of 10 is a straightforward process.
If you are dividing by 10, just move the decimal point one place to the left.
If you are dividing by 100, just move the decimal point 2 places to the left.
and so forth...
For
40
/
100
, the decimal point is after 0 for 40.
Moving that two places to the left bring the decimal point right before the 4.
A rational number can have either repeating decimal expansion or terminating decimal expansion
Repeating decimal expansion:
A decimal expansion in which the numbers repeat in exactly the same order
For example, 0.251251251251 is a repeating decimal expansion because 251 keeps repeating in the same order
Terminating decimal expansion:
A decimal expansion that ends in all zeros
For example, 0.150 is a terminating decimal expansion
Test your understanding of this lesson with the rational numbers quiz below.
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