Question

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

Decimals
ANSWERED
asked 2020-11-08
A true statement by inserting a symbol \(\displaystyle<,>{\quad\text{or}\quad}=\) between the given numbers 7.123 and \(\displaystyle\frac{456}{{64}}.\)

Answers (1)

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, \(\displaystyle{7.123}<\frac{456}{{64}}.\)
Answer:
\(\displaystyle{7.123}<\frac{456}{{64}}\)

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