Practice

Test what you understand. Start with the basics, then challenge yourself.

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Warm Up

Start with the ideas you already know.

Which of the following is an irrational number?

1/2 0.75 √2 7

Which of the following is a whole number?

−2 0 −1/2 √2

Which number system includes both positive and negative whole numbers?

Natural Numbers Whole Numbers Rational Numbers Integers

Which statement is true?

There is no largest Natural Number. 0 is a Natural Number. Every irrational number is rational. Negative numbers are whole numbers.

Apply the Idea

Use the rules instead of simply recalling them.

Which fraction has a terminating decimal representation?

1/3 1/6 3/8 2/15

Which of the following can be written in the form p/q, where p and q are integers and q ≠ 0?

√2 −5/3 π √5

What happens when 1 − 5 is calculated?

A negative number is needed. Zero is needed. A Natural Number is enough. The calculation is impossible.

Which statement about 6 is correct?

6 is irrational. 6 cannot be written as a fraction. 6 is not a real number. 6 can be written as 6/1.

Which of the following is a real number?

√2 3/4 Both √2 and 3/4 Neither

Think About It

Some questions need a little more reasoning.

A student says, “0.333... is irrational because its decimal representation never ends.” Is the student correct?

Yes, because it never ends. No, because it is equal to 1/3. Yes, because repeating decimals are irrational. No, because all decimals are irrational.

Which denominator will produce a terminating decimal after the fraction is in simplest form?

40 15 21 14

Why can a whole number also be considered a rational number?

Because every whole number is irrational. Because every whole number has a decimal. Because any whole number n can be written as n/1. Because zero is irrational.

Which statement is always true?

Every non-terminating decimal is irrational. Every decimal is rational. Every repeating decimal is irrational. Every terminating decimal is rational.

Challenge

Put several ideas together.

Without converting it to a decimal, determine whether 21/40 has a terminating decimal representation.

No, because 40 is not a prime number. Yes, because 40 = 2³ × 5. No, because 40 contains 2. Yes, because every fraction terminates.

If x = 0.777..., which equation helps eliminate the repeating decimal?

10x − x = 7 100x − x = 7 x − 10x = 7 10x + x = 7

Which statement best describes the relationship between Rational and Irrational Numbers?

Both are subsets of Integers. Both are subsets of Natural Numbers. Both are subsets of Real Numbers. Irrational Numbers are not Real Numbers.

PRACTICE COMPLETE

See how much you remember.

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Answer the questions above to see your result.

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