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Which number is greater?

In this educational resource, we explore how to compare rational and irrational numbers, focusing on students' understanding of radicals and integer exponents. We follow the reasoning of two students, Rodney and Sam, as they debate whether 4 or 17/4 is greater. Through step-by-step explanation using number lines and mathematical comparisons, students learn valuable skills in identifying greater and lesser values. Additional comparisons of numbers such as 2.89 with 3, and 5/11 with 0.4 reinforce these concepts.

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Which number is greater?

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  1. Which number is greater? Compare rational and irrational numbers.

  2. Focus 4 - Learning Goal #2:Students will work with radicals and integer exponents.

  3. Rodney thinks is greater than 17/4. Sam Thinks that 17/4is greater. Who is right and why? • = 4 • 17/4 = 4 ¼ • Because 4 < 4 ¼, then < 17/4. So, is smaller. • On a number line would be left of 17/4. • Therefore, Sam is correct. 4 ¼ 4 5

  4. Which number is smaller, or 2.89? Explain. • Because 2.89 <3, then 2.89 < . • On a number line, 2.89 is left of 3. • Therefore, 2.89 is smaller than . 2.89 2.5 3.5 3.0

  5. Which number is greater, or 319/45? Explain. • is irrational. • 7.1•7.1 = 50.41 • 7.09•7.09 = 50.2681 • 7.08•7.08 = 50.1264 • 7.07•7.07 = 49.9849 • is about 7.07 • 319/45 = 7 4/45 • 4/45 = .088888… • 319/45 is about 7.09. • Since 7.07 < 7.09, • then < 319/45. • The greater number is 319/45.

  6. Which number is greater,5/11or 0.4? Explain. • 5/11 is equal to 0.45 • Since 0.444444… < 0.4545454545…, • then 0.4 < 5/11. • The greater number is 5/11.

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