This worksheet gives 22 problems on rational and irrational numbers for Grade 8, standards 8.NS.A.1 and 8.NS.A.2. The first problems turn fractions into decimals and repeating decimals into fractions.
Next come square root estimates, number line plots and comparisons. The last six problems are word problems and reasoning tasks about garden beds, tile floors and common claims. Show every step.
Problem 1: Terminating decimal
Write \(\frac{3}{8}\) as a decimal. Tell whether the decimal terminates or repeats.
Problem 2: Repeating decimal
Write \(\frac{5}{9}\) as a decimal.
Problem 3: Two-digit repeat
Write \(\frac{7}{11}\) as a decimal.
Problem 4: Sort the numbers
Tell whether each number is rational or irrational: \(\sqrt{9}\), \(\sqrt{10}\), \(-\frac{4}{5}\), \(0.\overline{12}\), \(\pi\).
Problem 5: One repeating digit
Write \(0.\overline{4}\) as a fraction.
Problem 6: Two repeating digits
Write \(0.\overline{45}\) as a fraction in simplest form.
Problem 7: Three repeating digits
Write \(0.\overline{135}\) as a fraction in simplest form.
Problem 8: Delayed repeat
Write \(0.1\overline{6}\) as a fraction in simplest form.
Problem 9: Between two integers
Between which two consecutive integers is \(\sqrt{30}\)?
Problem 10: Nearest tenth
Estimate \(\sqrt{50}\) to the nearest tenth.
Problem 11: Square root of 2
Show that \(\sqrt{2}\) is between 1.41 and 1.42 by squaring.
Problem 12: Plot the root
Estimate \(\sqrt{5}\) and plot it on the number line.
Problem 13: Compare with a decimal
Compare \(\sqrt{7}\) and \(2.6\) using \(<\), \(>\) or \(=\).
Problem 14: Compare roots
Compare \(\sqrt{12}\) and \(3.5\).
Problem 15: Order four numbers
Write these numbers from least to greatest: \(\pi\), \(3.14\), \(\frac{22}{7}\), \(\sqrt{10}\).
Problem 16: Rational in between
Name a rational number between \(\sqrt{2}\) and \(\sqrt{3}\).
Problem 17: Square garden
Maya’s square garden bed has an area of 40 square feet. Estimate the side length to the nearest tenth of a foot.
Problem 18: Tile border
Jamal lays a square floor of tiles with an area of 90 square feet. Estimate the side length to the nearest tenth, then estimate the border length around the floor to the nearest foot.
Problem 19: Two lots
Diego’s square lot has an area of 45 square yards. Priya’s square lot has a side of 6.7 yards. Whose lot is larger? Explain.
Problem 20: Thirds and nines
Write \(0.\overline{3}\) and \(0.\overline{6}\) as fractions. Add the fractions and explain what the sum shows about \(0.\overline{9}\).
Problem 21: Square root claim
Ethan says that \(\sqrt{49}\) is irrational because it has a square root sign. Is he right? Explain.
Problem 22: Is 22/7 equal to pi?
Mei says that \(\frac{22}{7}\) is exactly equal to \(\pi\). Use decimals to show whether she is correct.
See every chapter on the Grade 8 math page.