Math Problem Statement

solve

Order these numbers from least to greatest: 6.50, 6 2/11, 6.185, 123/20.

Solution

To solve this problem, we need to order the given numbers from least to greatest. The numbers provided are:

  1. 6.506.50
  2. 62116 \frac{2}{11}
  3. 6.1856.185
  4. 12320\frac{123}{20}

Step 1: Convert all numbers to decimal form

  1. 6.50 is already in decimal form.
  2. 62116 \frac{2}{11} can be converted as follows: 6211=6+2116+0.1818=6.18186 \frac{2}{11} = 6 + \frac{2}{11} \approx 6 + 0.1818 = 6.1818
  3. 6.185 is already in decimal form.
  4. 12320\frac{123}{20} can be calculated as: 12320=6.15\frac{123}{20} = 6.15

Step 2: Compare the decimal values

The decimal equivalents are:

  • 6.506.50
  • 6.18186.1818
  • 6.1856.185
  • 6.156.15

Arranging these in ascending order gives:

  1. 6.156.15
  2. 6.18186.1818 (or 62116 \frac{2}{11})
  3. 6.1856.185
  4. 6.506.50

Final Order (from least to greatest)

The order from least to greatest is: 12320,6211,6.185,6.50\frac{123}{20}, \quad 6 \frac{2}{11}, \quad 6.185, \quad 6.50

Would you like more details on the conversions or have any questions?


Here are five related questions that might help deepen your understanding:

  1. How would the ordering change if we added a new number like 6.756.75?
  2. Can you explain why 62116 \frac{2}{11} is less than 6.1856.185 in decimal form?
  3. How can we convert fractions to decimals without a calculator?
  4. What is the significance of rounding in comparing decimal numbers?
  5. How would you compare two numbers if you only knew their fractions?

Tip: Converting all values to the same form (like decimals) is a useful strategy for comparison.

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Math Problem Analysis

Mathematical Concepts

Comparing Decimals and Fractions
Fraction to Decimal Conversion
Ordering Numbers

Formulas

Fraction to Decimal Conversion: a/b

Theorems

Properties of Inequality

Suitable Grade Level

Grades 6-8