Track quiz
Twelve ideas, twelve checks. Use the table if you get stuck.
| Idea | Remember |
|---|---|
| One shape | Any rational number is an integer over a non-zero integer. |
| No next door | Halfway between two fractions is another fraction. |
| Stopping | Cut down first. Only 2s and 5s in the bottom number make a decimal stop. |
| Repeating | A remainder that comes back makes every digit after it come back. |
| The road back | Two lines with the same tail, taken away, leave a whole number. |
| Irrational | A number that is not an integer over an integer. The diagonal of a unit square. |
| The argument | Suppose p/q is in lowest terms and squares to 2. Then p and q are both even. That is a clash. |
| The spiral | Each hypotenuse is the next leg. The square goes up by 1. |
| The squeeze | Square both ends of a gap and compare with the target. |
| Two names | The decimal 0.999… with endless 9s is exactly 1. A positive decimal that stops has a second name in endless 9s. |
| The cyclic block | Times 1 to 6, 142857 gives the same six digits, shifted. |
| Reading a decimal | A decimal that stops or repeats is rational. A decimal that never ends and never repeats is irrational. |
What is 2¼ as a fraction?
Which number is between 1/4 and 1/2?
Which fraction has a decimal that stops?
Dividing by 17, what is the most digits a block can have?
What fraction is 0.444…?
Which is true of √2?
In the √2 argument, p² = 2q². What does that say about p²?
At stage 4 of the spiral, the hypotenuse squares to 5. What does the next one square to?
Which gap holds √5?
What is 0.999… with endless 9s equal to?
What is 142857 × 6?
A decimal never ends and no block repeats. What is the number?
Chapter 3 is The World of Numbers. Read it and see where each idea appears.
Next: Exploring Algebraic Identities. Letters there stand for numbers like these.