Math Problem Statement

1.3 (Day 2) Compare and Order Rational and Irrational Numbers WS 24-25.pdf

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Solution

The document contains several exercises related to comparing and ordering rational and irrational numbers. Here are some of the tasks included:

  1. Estimate √48 by finding the integers it falls between and determining which integer it is closer to.
  2. Compare the numbers √3 and 2.6.
  3. Order the numbers 1,65,4,5,95,4.81, \frac{6}{5}, -4, \sqrt{5}, -\frac{9}{5}, 4.8 from least to greatest.
  4. Estimate √39 and find its position between two consecutive whole numbers, including refining the approximation by squaring decimals.
  5. Order the heights of clay pots with measurements: 23 in.,2.5 in.,1.2 in.,8 in.,1.8 in.,7 in.\frac{2}{3} \text{ in.}, 2.5 \text{ in.}, 1.2 \text{ in.}, \sqrt{8} \text{ in.}, 1.8 \text{ in.}, \sqrt{7} \text{ in.}

Would you like a detailed solution for one of these problems, or clarification on a specific part?

Here are five relative questions you might consider:

  1. How do you estimate square roots between integers?
  2. What are some tips for comparing irrational numbers to rational numbers?
  3. How do you approach ordering both positive and negative numbers?
  4. What is the best method to square decimals when refining square root estimates?
  5. How do you plot irrational numbers accurately on a number line?

Tip: When comparing square roots to integers or decimals, approximating the square roots can make it easier to compare!

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Math Problem Analysis

Mathematical Concepts

Square Root Estimation
Comparing Rational and Irrational Numbers
Ordering Numbers
Number Line Placement
Decimals and Fractions

Formulas

Estimation: √n falls between two integers m and n where m² < √n < n²
Inequalities: for comparing square roots and decimals

Theorems

Approximation Theorem for Irrational Numbers

Suitable Grade Level

Grades 7-9