Question
Compare and order 0.66…, and -0.6 and -6.6 from least to greatest
Answers
GPT-4o mini
To compare and order the numbers \( 0.66\ldots \), \(-0.6\), and \(-6.6\), let's first convert them into a form that is easy to compare.
1. The number \( 0.66\ldots \) is a repeating decimal that can be expressed as \( \frac{2}{3} \) (or approximately \( 0.6667 \)).
2. The number \(-0.6\) is simply \( -0.6 \).
3. The number \(-6.6\) is also straightforward as \( -6.6 \).
Now let's compare their values:
- \( -6.6 \) is the smallest since it is more negative than both \(-0.6\) and \( 0.66\ldots \).
- Next, we have \(-0.6\), which is less than \( 0.66\ldots \) since \(-0.6\) is negative and \( 0.66\ldots \) is positive.
- Finally, \( 0.66\ldots \) is the greatest since it is a positive value.
Putting these in order from least to greatest, we have:
\[
-6.6 < -0.6 < 0.66\ldots
\]
1. The number \( 0.66\ldots \) is a repeating decimal that can be expressed as \( \frac{2}{3} \) (or approximately \( 0.6667 \)).
2. The number \(-0.6\) is simply \( -0.6 \).
3. The number \(-6.6\) is also straightforward as \( -6.6 \).
Now let's compare their values:
- \( -6.6 \) is the smallest since it is more negative than both \(-0.6\) and \( 0.66\ldots \).
- Next, we have \(-0.6\), which is less than \( 0.66\ldots \) since \(-0.6\) is negative and \( 0.66\ldots \) is positive.
- Finally, \( 0.66\ldots \) is the greatest since it is a positive value.
Putting these in order from least to greatest, we have:
\[
-6.6 < -0.6 < 0.66\ldots
\]