Calculation:
To compare the numbers \(\displaystyle{0.58}\overline{{3}}{\quad\text{and}\quad}\frac{6}{{11}},\)
first we right the fraction \(\displaystyle\frac{6}{{11}}\) as decimal
and compare with the decimal \(\displaystyle{0.58}\overline{{3}}.\)
\(\displaystyle{11}\frac{0.5454}{{6.00}}\)
\(\displaystyle-\frac{55}{{50}}\)
\(\displaystyle-\frac{45}{{50}}\)
\(\displaystyle-\frac{45}{{50}}\)
\(\displaystyle-\frac{45}{{5}}\)
Therefore, \(\displaystyle\frac{6}{{11}}={0.545454}{\quad\text{or}\quad}{0}.\overline{{54}}\)
Now, we compare this with given decimal \(\displaystyle{0.58}\overline{{3}}.\)
Original numbers \(\displaystyle{0.58}\overline{{3}}\frac{6}{{11}}\)
Decimals \(\displaystyle{0.58}\overline{{3}}{0}.\overline{{54}}\)
Compare \(\displaystyle{0.58}\overline{{3}}>{0}.\overline{{54}}\)
Thus,\(\displaystyle{0.58}\overline{{3}}>\frac{6}{{11}}.\)
Answer: \(\displaystyle{0.58}\overline{{3}}>\frac{6}{{11}}\)
first we right the fraction \(\displaystyle\frac{6}{{11}}\) as decimal
and compare with the decimal \(\displaystyle{0.58}\overline{{3}}.\)
\(\displaystyle{11}\frac{0.5454}{{6.00}}\)
\(\displaystyle-\frac{55}{{50}}\)
\(\displaystyle-\frac{45}{{50}}\)
\(\displaystyle-\frac{45}{{50}}\)
\(\displaystyle-\frac{45}{{5}}\)
Therefore, \(\displaystyle\frac{6}{{11}}={0.545454}{\quad\text{or}\quad}{0}.\overline{{54}}\)
Now, we compare this with given decimal \(\displaystyle{0.58}\overline{{3}}.\)
Original numbers \(\displaystyle{0.58}\overline{{3}}\frac{6}{{11}}\)
Decimals \(\displaystyle{0.58}\overline{{3}}{0}.\overline{{54}}\)
Compare \(\displaystyle{0.58}\overline{{3}}>{0}.\overline{{54}}\)
Thus,\(\displaystyle{0.58}\overline{{3}}>\frac{6}{{11}}.\)
Answer: \(\displaystyle{0.58}\overline{{3}}>\frac{6}{{11}}\)
