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There Is Always Another Rational Number Between Two

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The World of Numbers · Rational numbers on the number line · 3:34

You'll learn: Use averaging to generate a number strictly between two distinct rational numbers.

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There Is Always Another Rational Number Between Two

3:34

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There Is Always Another Rational Number Between Two

You'll learn: Use averaging to generate a number strictly between two distinct rational numbers.

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Same topic

Rational numbers on the number line

4

Place Positive, Negative and Improper Fractions on a Line
3:23
Place Positive, Negative and Improper Fractions on a Line
You'll learn: Divide unit intervals equally and locate fractions on either side of zero.
Absolute Value Measures Distance, Not Direction
3:29
Absolute Value Measures Distance, Not Direction
You'll learn: Explain absolute value and distance between two rational points.
Find Several Rational Numbers in One Interval
3:40
Find Several Rational Numbers in One Interval
You'll learn: Use common denominators or repeated averaging to list the required number of interior points.
Find Numbers Between Very Close Decimals
3:44
Find Numbers Between Very Close Decimals
You'll learn: Refine decimal places to reveal rational values in a narrow interval.

Next topic

Rational-number applications

2

How Many Complete Kurtas Can the Tailor Make?
3:31
How Many Complete Kurtas Can the Tailor Make?
You'll learn: Divide mixed-number measurements and interpret a whole-object result.
Solve a Rational-Number Equation and Reason About Its Sign
3:18
Solve a Rational-Number Equation and Reason About Its Sign
You'll learn: Solve a fractional-coefficient equation and infer a product’s sign from a relation.

Next topic

Irrational lengths and proofs

7

A Unit Square Reveals a New Kind of Number
3:25
A Unit Square Reveals a New Kind of Number
You'll learn: Use the diagonal of a unit square to motivate √2 and irrational numbers.
Why √2 Cannot Be a Fraction
3:25
Why √2 Cannot Be a Fraction
You'll learn: Follow the contradiction proof from a lowest-terms fraction to both numerator and denominator being even.
Extend the Irrationality Proof to Other Square Roots
4:00
Extend the Irrationality Proof to Other Square Roots
You'll learn: Adapt the contradiction method and identify the divisibility step needed.
Construct √2 and Transfer It to the Number Line
3:24
Construct √2 and Transfer It to the Number Line
You'll learn: Build a right triangle and use a compass arc to locate the exact irrational length.
Build More Square Roots with a Square Root Spiral
3:51
Build More Square Roots with a Square Root Spiral
You'll learn: Extend successive unit-perpendicular triangles and identify hypotenuse lengths.
Pi: An Exact Number with Fractional Approximations
3:27
Pi: An Exact Number with Fractional Approximations
You'll learn: Define π as circumference divided by diameter and distinguish exact π from a rational approximation.
How Can Adding More Terms Approach Pi?
3:32
How Can Adding More Terms Approach Pi?
You'll learn: Explore the chapter’s alternating infinite-series example through finite partial sums.

Next topic

Real numbers and decimal expansions

2

Rational and Irrational Numbers Share One Real Number Line
3:44
Rational and Irrational Numbers Share One Real Number Line
You'll learn: Connect natural numbers, integers, rationals, irrationals and reals in a nested classification.
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.