Studdy AI Logo
Math  /  Numbers & Operations

QuestionPut these numbers in order from least to greatest. −616-\frac{61}{6} −2-2 −133-\sqrt{133}

Studdy Solution

STEP 1

1. Each number needs to be converted to a comparable form (either decimal or fractional) for easier comparison.
2. Negative numbers are smaller than positive numbers, and among negative numbers, those with larger absolute values are smaller.
3. 133\sqrt{133} is an irrational number, which can be approximated to a decimal for comparison.

STEP 2

1. Convert −616-\frac{61}{6} to decimal form.
2. Convert −2-2 to decimal form (if necessary).
3. Approximate −133-\sqrt{133} to a decimal.
4. Compare the decimal forms of all three numbers.
5. Arrange the numbers in order from least to greatest.

STEP 3

Convert −616-\frac{61}{6} to decimal form.
−616≈−10.1667 -\frac{61}{6} \approx -10.1667

STEP 4

Convert −2-2 to decimal form.
−2=−2.0 -2 = -2.0

STEP 5

Approximate −133-\sqrt{133} to a decimal.
133≈11.54 \sqrt{133} \approx 11.54 −133≈−11.54 -\sqrt{133} \approx -11.54

STEP 6

Compare the decimal forms of the numbers obtained: −616≈−10.1667 -\frac{61}{6} \approx -10.1667 −2.0 -2.0 −133≈−11.54 -\sqrt{133} \approx -11.54
From the approximations: −11.54<−10.1667<−2.0 -11.54 < -10.1667 < -2.0
Therefore, from least to greatest: −133,−616,−2 -\sqrt{133}, -\frac{61}{6}, -2

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord