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# A true statement by inserting a symbol displaystyle<,>{quadtext{or}quad}= between the given numbers displaystyle{0.58}overline{{3}}{quadtext{and}quad}frac{6}{{11}}

Question
Decimals
asked 2020-11-08
A true statement by inserting a symbol $$\displaystyle<,>{\quad\text{or}\quad}=$$ between the given numbers $$\displaystyle{0.58}\overline{{3}}{\quad\text{and}\quad}\frac{6}{{11}}$$

## Answers (1)

2020-11-09
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: $$\displaystyle{0.58}\overline{{3}}>\frac{6}{{11}}$$

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