Math Problem Statement

Which number comes first when the numbers are listed from least to greatest? 1/6, -3, sqrt(7), -6/5, 3.9

Solution

Let's go step by step to find the correct order of these numbers from least to greatest, and answer which comes first:

The numbers provided are: 16,3,7,65,3.9\frac{1}{6}, -3, \sqrt{7}, -\frac{6}{5}, 3.9

Step 1: Converting all values into decimal form

  1. 160.1667\frac{1}{6} \approx 0.1667
  2. 3-3 (already in decimal form)
  3. 72.6458\sqrt{7} \approx 2.6458
  4. 65=1.2-\frac{6}{5} = -1.2
  5. 3.93.9 (already in decimal form)

Step 2: Ordering the numbers

From least to greatest:

  • The most negative number is 3-3.
  • Next comes 65=1.2-\frac{6}{5} = -1.2.
  • The smallest positive number is 160.1667\frac{1}{6} \approx 0.1667.
  • Then comes 72.6458\sqrt{7} \approx 2.6458.
  • Finally, 3.93.9 is the largest.

Step 3: Answer the question

The number that comes first when listed from least to greatest is 3-3.

Correct choice:

The correct answer is D. 3-3 because it is the negative number with the greatest absolute value.

Would you like more details on any part of this solution?


Here are 5 related questions to expand your understanding:

  1. How do you compare numbers with different forms (fractions, square roots, etc.)?
  2. How can absolute value help when comparing negative numbers?
  3. What is the approximate value of 2,3,5\sqrt{2}, \sqrt{3}, \sqrt{5}, etc.?
  4. How do you convert fractions to decimals?
  5. What is the role of irrational numbers (like 7\sqrt{7}) in number comparison?

Tip: When comparing numbers, converting them all to the same form (usually decimals) can make the process easier.

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Math Problem Analysis

Mathematical Concepts

Number comparison
Absolute values
Decimals and fractions

Formulas

Conversion of fractions to decimals
Square root approximations

Theorems

Ordering of real numbers

Suitable Grade Level

Grades 6-8