Question

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

Decimals
ANSWERED
asked 2021-01-15
To make: A true statement by inserting a symbol \(<,\ >\ or\ =\ \text{between the given numbers}\ \displaystyle\overline{{0.6}}{\quad\text{and}\quad}\frac{5}{{6}}.\)

Answers (1)

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 \(\displaystyle\overline{{0.6}}<\overline{{0.83}}\)
Thus, \(\displaystyle\overline{{0.6}}<\frac{5}{{6}}.\)
Final statement:
\(\displaystyle\overline{{0.6}}<\frac{5}{{6}}.\)

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