Question

# A true statement by inserting a symbol displaystyle<,>{quadtext{or}quad}= between the given numbers 7.123 and displaystylefrac{456}{{64}}.

Decimals
A true statement by inserting a symbol $$\displaystyle<,>{\quad\text{or}\quad}=$$ between the given numbers 7.123 and $$\displaystyle\frac{456}{{64}}.$$

2020-11-09

Given numbers:
$$\displaystyle{7.123}{\quad\text{and}\quad}\frac{456}{{64}}.$$
For compare this numbers, we write the fraction $$\displaystyle\frac{456}{{64}}$$ as decimal and compare with the decimal 7.123.
$$\displaystyle{64}\frac{7.125}{{456.00}}$$
$$\displaystyle-\frac{448}{{80}}$$
$$\displaystyle-\frac{64}{{160}}$$
$$\displaystyle-\frac{128}{{320}}$$
$$\displaystyle-\frac{320}{{0}}$$
Hence, $$\displaystyle\frac{456}{{64}}={7.125}.$$
Now, we compare this given decimal 7.123.
Original numbers $$\displaystyle{7.123}\frac{4}{{64}}$$
Decimals 7.123 7.125
Compare $$\displaystyle{7.123}<{7.125}$$
Thus, $$\displaystyle{7.123}<\frac{456}{{64}}.$$
$$\displaystyle{7.123}<\frac{456}{{64}}$$