Rational numbers on a number line – comparing and zooming in
MathematicsNumbers & ArithmeticAges 12–13
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Numbers & Arithmetic
Two rational numbers a and b (entered as p/q or a decimal) are marked on a number line; the zoomed-in axis below is divided by their common denominator to show why a < b or a > b. Drag point a or b to change its value (snapping to the tick marks), view the decimal form, and see that the midpoint (a+b)/2 is always a rational number lying between the two. The Decimal expansion screen divides p by q step by step, tracks each remainder until one repeats, explains when a decimal terminates, and converts recurring decimals to fractions by the algebraic method.
Lesson: Rational numbers; representing and comparing rational numbers on a number line
What it shows
Every rational number p/q has an exact place on the number line, found by dividing each unit into q equal parts. The Number line screen rewrites two fractions over their lowest common denominator, so their order can be read from the numerators, and the midpoint (a + b)/2 shows that between two rationals there is always another. The Decimal expansion screen carries out the long division of p by q. Only q remainders are possible, so the digits either stop, exactly when q in lowest terms has no prime factors other than 2 and 5, or repeat. The algebraic method turns a recurring decimal into a fraction.
How to use
On the Number line screen, type Number a and Number b as fractions or decimals or use the example buttons; Zoom in shows the common-denominator axis and Decimal the decimal forms. Drag a or b along either axis. On the Decimal expansion screen, set Numerator p and Denominator q, then use Next step or Play and watch the remainders until one repeats. Type a recurring decimal such as 0.1(6) to follow the algebraic method.
Parameters you can change
- Number a (as p/q or decimal)
- Number b (as p/q or decimal)
- Show zoomed-in axis by common denominator
- Show decimal form
- Screen Number line, Decimal expansion
- Numerator p (Decimal expansion screen) 1–999
- Denominator q (Decimal expansion screen) 2–99
- Recurring decimal to convert, repeating block in brackets (Decimal expansion screen)
Questions to explore
- Using the zoomed-in axis, which is greater, −2/3 or −3/4, and why?
- Find three rational numbers between 1/3 and 1/2. How can the midpoint help you?
- Why does 2/3 have a repeating decimal form while 3/4 has a terminating one?
