Real Numbers — Drills
Real Numbers has 3 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 6 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Integer — A whole number, positive, negative, or zero.
- π — The circumference of any circle divided by its diameter — about 3.14159.
- Perfect square — A number that is some whole number squared: 1, 4, 9, 16, 25, …
- Square root — For k ≥ 0, √k is the nonnegative number whose square is k.
- Rational — Any number writable as ab with integers a and b, b ≠ 0.
- Irrational — A real number that cannot be written as a fraction — its decimal never repeats and never ends.
Classifying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Classify √81.
- Rational
- Irrational
Worked answer
Rational
√81 = 9, a whole number, so rational.
Problem 2
Classify √49.
- Rational
- Irrational
Worked answer
Rational
√49 = 7, a whole number, so rational.
Repeating
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write 0.56 as a fraction in lowest terms.
Worked answer
56/99
Let x = 0.5656…, so 100x = 56.56…
99x = 56
x = 5699 = 5699
Problem 2
Write 0.43 as a fraction in lowest terms.
Worked answer
43/99
Let x = 0.4343…, so 100x = 43.43…
99x = 43
x = 4399 = 4399
Ordering
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which is largest?
- √0.8229
- 67
- 0.80
Worked answer
√0.8229
67 ≈ 0.857
0.80 ≈ 0.800
√0.8229 ≈ 0.907
Largest is √0.8229.