Rational Number on the Line

A rational number is any number you can write as p/q where p and q are integers and q is not zero. So 3/4, -5/2 and 7 (which is 7/1) are all rational. The lab plots p/q on the number line for any chosen p and q.

Slide numerator p between -20 and 20 and denominator q between 1 and 20. The lab shows the decimal value p/q and its additive inverse -p/q. Try p = 3, q = 4 to see 0.75 and -0.75.

Yes, every fraction with integer top and non-zero integer bottom is rational. But not every decimal is rational; numbers like pi or root 2 cannot be written as p/q. The lab sticks to safe rational values you can see exactly.

Every integer is rational (5 = 5/1), but not every rational is an integer (1/2 is not). Set q = 1 in the lab and you only see integers; set q to bigger numbers and you get fractions between the integers, like 1.5 or -3/7.