Grade 8 · Math

8th grade Kinds of real numbers: rational and irrational worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Kinds of real numbers: rational and irrational

Grade 8 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

1.
Bo copies a long decimal into a notebook. Point P is the number 2.1666…, and its digits repeat the digit 6 forever. What is the smallest group that holds P?
- irrational numbers
- rational numbers
- integers
2.
Jun checks a decimal in a math book. Point P is the number 0.125, and its digits stop after the 5. What is the smallest group that holds P?
- rational numbers
- integers
- irrational numbers
3.
Luz scrolls through a screen full of digits. Point P is the number 2.6457513…, and its digits never end and never repeat. What is the smallest group that holds P?
- integers
- irrational numbers
- rational numbers
4.
Milo writes 6.0 in a score box. Point P is the number 6.0, and its digits are a 6, a point and a 0, and nothing more. What is the smallest group that holds P?
- integers
- whole numbers
- rational numbers
- irrational numbers
5.
Noah puts √49 on a number line for a poster. The figure shows whole numbers multiplied by themselves. What is the smallest group that holds √49?
- irrational numbers
- rational numbers
- whole numbers
6.
Pia wants to place √20 on a number line. The figure shows whole numbers multiplied by themselves. What is the smallest group that holds √20?
- rational numbers
- irrational numbers
- whole numbers
Read this first
Use this
Number line from 0 to 13, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Check: 12 × 12 = 144. P is the mark √144.
7.
Ren is checking √144 for a puzzle. The figure shows whole numbers multiplied by themselves. What is the smallest group that holds √144?
- rational numbers
- irrational numbers
- whole numbers
8.
Tala marks √12 on a chalk number line. The figure shows whole numbers multiplied by themselves. What is the smallest group that holds √12?
- rational numbers
- irrational numbers
- whole numbers
9.
Ari has √121 on a puzzle card. The figure shows whole numbers multiplied by themselves. What is the smallest group that holds √121?
- whole numbers
- rational numbers
- irrational numbers
10.
Bo finds √90 in a math game. The figure shows whole numbers multiplied by themselves. What is the smallest group that holds √90?
- irrational numbers
- whole numbers
- rational numbers

8th grade Kinds of real numbers: rational and irrational worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Kinds of real numbers: rational and irrational. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can tell whether a number is rational or irrational and say why: its decimal stops or repeats, or it never ends and never repeats.
I can name the smallest group that holds a number, or a whole list of numbers, and I know the rational and irrational numbers together make up the real numbers.

Standard: 8.NS.A.1 (irrational numbers)

Words to know

rational number: A number you can write as a fraction. Its decimal stops or repeats.

irrational number: A number with a decimal that never ends and never repeats, like π.

real number: Any number that has a mark on the number line.

perfect square: A number you get by multiplying a whole number by itself: 49 = 7 × 7.

square root (√): The number that, multiplied by itself, gives the number under the sign.

repeating decimal: A decimal with a block of digits that repeats forever, like 0.4545….

Common mistakes

Your child treated every square root as irrational.

Your child read a calculator's short decimal for a square root as if it ended.

Your child rounded a square root to a whole number and called it whole.

What to say

Ask: what is the square root of 49? Does it come out exactly?

Ask: do the digits of the square root of 2 stop, or do they keep going with no pattern?

Ask: is the square root of 20 exactly 4 or exactly 5?

Questions parents ask

What is the most common mistake with kinds of real numbers: rational and irrational?

Your child treated every square root as irrational.

How can I help my child with kinds of real numbers: rational and irrational?

Ask: what is the square root of 49? Does it come out exactly?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

See all grade 8 math

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