Question
is 6 1/11 repeating?
Answers
Answer
what about 4 33/100
Answer
what about 32/9
Answer
last one 23/6?
Answered by
GPT-4o mini
The number \(6 \frac{1}{11}\) is a mixed number, which can also be expressed as an improper fraction. To do this, convert the mixed number into an improper fraction:
\[
6 \frac{1}{11} = \frac{6 \times 11 + 1}{11} = \frac{66 + 1}{11} = \frac{67}{11}
\]
The fraction \(\frac{67}{11}\) can be converted to a decimal by performing the division \(67 \div 11\).
When you divide \(67\) by \(11\), you get:
\[
67 \div 11 = 6.090909...
\]
The decimal \(6.090909...\) has the digit sequence \(09\) repeating indefinitely. Therefore, \(6 \frac{1}{11}\) can be expressed as:
\[
6.09\overline{09}
\]
In conclusion, yes, \(6 \frac{1}{11}\) does have a repeating decimal part, which is the \(09\) that repeats.
\[
6 \frac{1}{11} = \frac{6 \times 11 + 1}{11} = \frac{66 + 1}{11} = \frac{67}{11}
\]
The fraction \(\frac{67}{11}\) can be converted to a decimal by performing the division \(67 \div 11\).
When you divide \(67\) by \(11\), you get:
\[
67 \div 11 = 6.090909...
\]
The decimal \(6.090909...\) has the digit sequence \(09\) repeating indefinitely. Therefore, \(6 \frac{1}{11}\) can be expressed as:
\[
6.09\overline{09}
\]
In conclusion, yes, \(6 \frac{1}{11}\) does have a repeating decimal part, which is the \(09\) that repeats.
Answered by
GPT-4o mini
The number \(4 \frac{33}{100}\) is another mixed number. To analyze whether it is repeating, let's convert it into an improper fraction and then to a decimal.
1. Convert the mixed number to an improper fraction:
\[
4 \frac{33}{100} = \frac{4 \times 100 + 33}{100} = \frac{400 + 33}{100} = \frac{433}{100}
\]
2. Now convert the improper fraction to a decimal by performing the division \(433 \div 100\):
\[
433 \div 100 = 4.33
\]
The decimal \(4.33\) terminates and does not have any repeating digits.
In summary, \(4 \frac{33}{100}\) as a decimal is \(4.33\), which is not a repeating decimal.
1. Convert the mixed number to an improper fraction:
\[
4 \frac{33}{100} = \frac{4 \times 100 + 33}{100} = \frac{400 + 33}{100} = \frac{433}{100}
\]
2. Now convert the improper fraction to a decimal by performing the division \(433 \div 100\):
\[
433 \div 100 = 4.33
\]
The decimal \(4.33\) terminates and does not have any repeating digits.
In summary, \(4 \frac{33}{100}\) as a decimal is \(4.33\), which is not a repeating decimal.
Answered by
GPT-4o mini
To determine whether the fraction \(\frac{32}{9}\) is repeating or terminating, we can convert it to a decimal by performing the division.
Dividing \(32\) by \(9\):
\[
32 \div 9 = 3.5555\ldots
\]
This can also be expressed as:
\[
3.\overline{5}
\]
Here, the digit \(5\) repeats indefinitely.
Thus, \(\frac{32}{9}\) as a decimal is \(3.\overline{5}\), which means it is a repeating decimal.
Dividing \(32\) by \(9\):
\[
32 \div 9 = 3.5555\ldots
\]
This can also be expressed as:
\[
3.\overline{5}
\]
Here, the digit \(5\) repeats indefinitely.
Thus, \(\frac{32}{9}\) as a decimal is \(3.\overline{5}\), which means it is a repeating decimal.
Answered by
GPT-4o mini
To determine whether the fraction \(\frac{23}{6}\) has a terminating or repeating decimal, we can convert it to a decimal by performing the division.
Dividing \(23\) by \(6\):
\[
23 \div 6 = 3.8333\ldots
\]
This can also be expressed as:
\[
3.8\overline{3}
\]
The digit \(3\) repeats indefinitely.
Thus, \(\frac{23}{6}\) as a decimal is \(3.8\overline{3}\), which means it is a repeating decimal.
Dividing \(23\) by \(6\):
\[
23 \div 6 = 3.8333\ldots
\]
This can also be expressed as:
\[
3.8\overline{3}
\]
The digit \(3\) repeats indefinitely.
Thus, \(\frac{23}{6}\) as a decimal is \(3.8\overline{3}\), which means it is a repeating decimal.
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