# To make: A true statement by inserting a symbol <, > or = text{between the given numbers} displaystyleoverline{{0.6}}{quadtext{and}quad}frac{5}{{6}}.

Question
Decimals
To make: A true statement by inserting a symbol $$<,\ >\ or\ =\ \text{between the given numbers}\ \displaystyle\overline{{0.6}}{\quad\text{and}\quad}\frac{5}{{6}}.$$

2021-01-16
The given numbers are $$\bar{0.6}\ and\ \frac{5}{6}.$$
To compare the numbers $$\displaystyle\overline{{0.6}}{\quad\text{and}\quad}\frac{5}{{6}},\ \text{first we write the fraction}\ \frac{5}{6}\ \text{as decimal and compare with the decimal}\ \bar{0.6}.$$
$$\displaystyle{6}\frac{0.833}{{5.00}}$$
$$\displaystyle\frac{{-{48}}}{{20}}$$
$$\displaystyle\frac{{-{18}}}{{20}}$$
$$\displaystyle\frac{{-{18}}}{{20}}$$
$$\displaystyle\frac{{-{18}}}{{2}}$$
Thus, $$\displaystyle\frac{5}{{6}}={0.833}\ldots{\quad\text{or}\quad}\overline{{0.83}}.$$
Now, we compare this with given decimal $$\bar{0.6}.$$
Original number $$\displaystyle\overline{{0.6}}\frac{5}{{6}}$$
Decimals$$\displaystyle\overline{{0.6}}\overline{{0.83}}$$
Compare $$\displaystyle\overline{{0.6}}<\overline{{0.83}}$$</span>
Thus, $$\displaystyle\overline{{0.6}}<\frac{5}{{6}}.$$</span>
Final statement:
$$\displaystyle\overline{{0.6}}<\frac{5}{{6}}.$$</span>

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