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Rational and Irrational Numbers

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Rational and Irrational Numbers

Help a math club sort numbers for a display. A rational number can be written as a fraction of integers; its decimal terminates or repeats. An irrational number has a decimal that neither terminates nor repeats. Show your reasoning when asked.

Sort the Numbers

Use the number clues to decide which display card belongs in each category.

1.Which number is irrational?

−3
0.4
√16
√7

2.The club's calculator shows 0.272727… with the digits 27 repeating forever. Is this number rational or irrational? Explain using the decimal pattern.

3.Select every rational number for the club's rational-number tray.

√25
π
−7/3
0.1010010001… (the gaps between 1s keep growing)
1.625

4.True or false: Every non-terminating decimal is irrational. Correct the statement if it is false.

TrueFalse

5.Complete the rule: A decimal that terminates or is rational.

Explain and Place

Use exact values and decimal clues to justify your decisions.

6.Match each number to its best description.

√36
0.125
π
5/9

B. Rational: perfect-square root
A. Irrational: non-terminating, non-repeating decimal
C. Rational: terminating decimal
D. Rational: fraction of integers

7.A student says √49 is irrational because it has a radical sign. Decide whether the student is correct. Explain why.

8.Put 1.5, √3, and π in order from least to greatest on the number line. Use approximate values to help.

9.A mystery decimal begins 0.101001000100001… . Each new 1 has more zeros before it. Based on this pattern, classify the number and explain your choice.

10.The display needs one new example of each type. Give a rational number that is not an integer and an irrational number between 2 and 4. Briefly justify both choices.