VaaraVaara Classroom

Videos Practice Progress

Loading video…

Loading…

Loading video…

Rational and Irrational Numbers Share One Real Number Line

Ask Vaara

Your maths helper for this video

Loading…

The World of Numbers · Real numbers and decimal expansions · 3:44

You'll learn: Connect natural numbers, integers, rationals, irrationals and reals in a nested classification.

Up next

15 videos

Now playing

Rational and Irrational Numbers Share One Real Number Line

3:44

Playing

Rational and Irrational Numbers Share One Real Number Line

You'll learn: Connect natural numbers, integers, rationals, irrationals and reals in a nested classification.

Now playing

Same topic

Real numbers and decimal expansions

12

Why Rational Decimals Either Stop or Repeat
3:30
Why Rational Decimals Either Stop or Repeat
You'll learn: Distinguish terminating decimals from repeating ones and use long division.
Repeated Remainders Make Repeated Digits
3:39
Repeated Remainders Make Repeated Digits
You'll learn: Explain why a long-division process eventually terminates or cycles.
Predict a Terminating Decimal Without Dividing
3:41
Predict a Terminating Decimal Without Dividing
You'll learn: Reduce a fraction first, then inspect prime factors of its denominator.
How Many Decimal Places Will a Fraction Need?
3:39
How Many Decimal Places Will a Fraction Need?
You'll learn: Balance powers of 2 and 5 to turn a reduced denominator into a power of ten.
Turn a Terminating Decimal into a Fraction
3:42
Turn a Terminating Decimal into a Fraction
You'll learn: Use place value to write a power-of-ten denominator and reduce.
Turn a Pure Repeating Decimal into a Fraction
3:32
Turn a Pure Repeating Decimal into a Fraction
You'll learn: Multiply by a power of ten matching the cycle length, subtract and solve.
A Non-Repeating Start Followed by One Repeating Digit
3:46
A Non-Repeating Start Followed by One Repeating Digit
You'll learn: Align repeating tails after moving the non-repeating prefix.
Convert a Mixed Decimal with a Repeating Block
3:50
Convert a Mixed Decimal with a Repeating Block
You'll learn: Extend tail alignment to a multi-digit repeating cycle and select the correct powers of ten.
Why the Digits 142857 Keep Rotating
3:34
Why the Digits 142857 Keep Rotating
You'll learn: Explore a cyclic number arising from the repeating block of 1/7.
Investigate the Repeating Blocks of Thirteenths
3:37
Investigate the Repeating Blocks of Thirteenths
You'll learn: Compute and compare repeating blocks for successive multiples of 1/13.
A Decimal Can Have a Pattern Without Repeating
3:55
A Decimal Can Have a Pattern Without Repeating
You'll learn: Classify rational and irrational numbers using exact form and decimal behaviour.
Why 0.999… Is Exactly 1
3:36
Why 0.999… Is Exactly 1
You'll learn: Use algebraic cancellation to prove equality and explain two decimal representations of terminating values.

Next topic

Closing perspective

1

Why √−1 Is Not on the Real Number Line
2:59
Why √−1 Is Not on the Real Number Line
You'll learn: Explain why squaring any real number cannot produce −1 and introduce the chapter’s final question.

Next topic

Chapter challenge problems

2

Find More Reciprocals with Cyclic Repeating Blocks
3:46
Find More Reciprocals with Cyclic Repeating Blocks
You'll learn: Test reciprocal decimals and compare rotations of their repeating blocks.
What Does the Fourth Decimal Place Tell Us?
3:38
What Does the Fourth Decimal Place Tell Us?
You'll learn: Relate a last non-zero fourth decimal digit to a numerator over 10⁴ and examine reduction.