Math Problem Statement
Solution
The problem asks you to compare three numbers: , , and , using the given number line ranging from 0 to 4.
Step 1: Calculate the approximate values of the numbers
- (since )
- (since )
Step 2: Place these values on the number line
- is slightly above 3.
- is located between 2 and 3, closer to 3.
- is located between 2 and 3, but closer to 2.
Step 3: Compare the numbers
We can now compare their positions:
- is the smallest.
- Next is .
- Finally, is the largest.
Step 4: Analyze the answer choices
- A. — Incorrect, because .
- B. — Correct, because and .
- C. — Incorrect, because .
- D. — Incorrect, because .
Correct Answer: B
Would you like more details or have any questions?
Here are 5 related questions:
- How do you approximate square roots without a calculator?
- Why is an irrational number, and how is it represented on a number line?
- Can be expressed as a mixed fraction, and what would it be?
- How does the number line help in comparing decimal approximations?
- What are the common ways to estimate fractions like ?
Tip: When comparing fractions, convert them to decimals to easily position them on a number line.
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Math Problem Analysis
Mathematical Concepts
Number Line
Decimal Approximation
Square Roots
Fractions
Irrational Numbers
Formulas
π ≈ 3.1416
√7.29 = 2.7
16/7 ≈ 2.2857
Theorems
Square Root Calculation
Fraction to Decimal Conversion
Suitable Grade Level
Grades 6-8
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