Step by step
The question
Question: is 7/9 rational or irrational?
79
Rational means: it can be written as a fraction, with whole numbers on top and at the bottom.
Then its decimal stops, or repeats for ever.
Irrational means: no fraction works.
Its decimal never stops and never repeats.
rational = a fraction of whole numbers
decimal stops or repeats
1 Look at the fraction
It is already a fraction.
The top, 7, and the bottom, 9, are whole numbers.
top 7, bottom 9: whole numbers
Careful!
The decimal may go on for ever.
That is fine, if it repeats.
Rational only asks for a fraction.
Careful: its decimal may go on, but it repeats
So 7/9 is rational.
A fraction of whole numbers is rational.
= 79 is rational
2 Check
Let's check with the decimal: 7 divided by 9 is 0.777777, and so on.
It repeats.
So the answer is right!
7 ÷ 9 = 0.777777…
Let's look back.
First: look at the fraction.
Last: check.
Answer
= 79 is rational