CCSS 8.NS.1 Worksheets

CCSS 8.NS.1 (Common Core, 8th Grade): "Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number." The worksheets below practice this standard. Each one is a free printable PDF with an answer key, comes in multiple versions, and can also be assigned digitally - no login or account needed.

The Number System Know that there are numbers that are not rational, and approximate them by rational numbers. 1Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

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Identifying Rational and Irrational Numbers

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• Decide whether a number is rational or irrational.
• Recognize that fractions, integers, and whole numbers are rational because they can be written as a ratio of integers.
• Tell that terminating decimals and repeating decimals are rational numbers.
• Identify common irrational numbers like pi and square roots that do not simplify to a fraction.

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Converting Repeating Decimals to Fractions

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• Recognize when a decimal repeats and identify the repeating part.
• Convert a repeating decimal into a fraction using an equation and solving for the value.
• Explain why repeating decimals represent rational numbers.

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Classifying Numbers as Rational or Irrational

8ns1

• Classify numbers as rational or irrational.
• Recognize that square roots of non-perfect squares and multiples of pi are irrational.
• Recognize that fractions, terminating decimals, integers, and square roots of perfect squares are rational.