Alberta Grade 8 Math — Unit: Rational & Irrational Numbers
Organizing IdeaNumber — Number sense is developed through understanding the ways numbers describe the world.
Learning OutcomeStudents interpret rational and irrational numbers.
This lesson covers: converting fractions to terminating or repeating decimals using long division;
recognizing repeating decimals using bar notation; understanding why a fraction terminates (denominator factors of only 2 and 5).
Every Fraction is a Division
The fraction bar literally means divide. When you write 3⁄4,
you’re asking: “3 divided by 4”.
Every rational number has a decimal form — and that decimal is always
either terminating (stops) or repeating (a block of digits cycles forever).
34
= 3 ÷ 4
0.75
terminates
13
= 1 ÷ 3
0.3
repeating
58
= 5 ÷ 8
0.625
terminates
56
= 5 ÷ 6
0.83
repeating
Bar notation puts a bar over the repeating block:
0.3 means 0.3333…,
and 0.142857 means 0.142857142857…
Only the digits under the bar repeat.
Watch the Long Division
Pick a fraction — then watch each step of the division appear one at a time.
Notice when remainders repeat: that’s what creates the repeating decimal.
The Secret Rule
You don’t need to divide to predict terminating vs repeating.
First reduce the fraction to lowest terms.
Then look at the prime factors of the denominator:
Only 2s and 5s? → terminates (because 2s and 5s make 10s). Any other prime? → repeating.
Pick a fraction above to see why it terminates or repeats.
Watch out: reduce first! 2⁄6 looks like it has a 3 in the denominator,
but 2⁄6 = 1⁄3 (a 3 — repeating). And 4⁄10 = 2⁄5
(only 5 — terminates, giving 0.4).
Round 1 of 3
Simple Fractions
Will it terminate or repeat? Then check the decimal.