Practice question · Match the pairs
Match each number or term to its defining feature.
- 1/4
- 1/7
- The square root of 2
- Lowest terms
- Numerator and denominator have gcd 1
- Terminating decimal
- Repeating decimal with a block of length 6
- Irrational, proved by contradiction
Hints
- Two of these are rational numbers distinguished only by how their decimals behave.
- Only one entry is not a number at all.
Show the answer
- 1/4 → Terminating decimal
- 1/7 → Repeating decimal with a block of length 6
- The square root of 2 → Irrational, proved by contradiction
- Lowest terms → Numerator and denominator have gcd 1
Why
1/4 = 0.25 terminates because 4 uses only the prime 2; 1/7 repeats with period 6 because 7 divides no power of ten. The square root of 2 escapes the rationals entirely, and lowest terms is the unique reduced representative of a rational.
Practise Rational and Irrational Numbers
The app has 4 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
More questions on Rational and Irrational Numbers
- The classic proof that √2 is irrational assumes a fraction in lowest terms and derives that both numerator…
- Write 84/126 in lowest terms. What is the numerator of the reduced fraction?
- Sort each number by whether it is rational or irrational.
- Order the steps of the proof by contradiction that the square root of 2 is irrational.
- Complete the characterization of irrational numbers.
- Between any two rationals lies another rational, so they leave no gaps you can point to. Yet they have gaps.…
- Compute 2/3 + 3/4 and write the result in lowest terms. What is the numerator?
- Select every statement that is TRUE.