Question

What type of decimal expansion does 63 by 72 into 175 have?

Answer 1

so the decimal expansion is 153.125 .

Answer 2

A decimal with an end digit is known as a terminating decimal. It's a decimal number with a limited number of digits (or terms). For example,  $0.15,0.86$, and so on. The term "non-terminating decimal" refers to a decimal that does not have an end term. For example $0.3333,$ $0.1827518275$

Given: $\frac{63}{72}\times 175$

If any denominator can be written in form $(2\times 5)^n$  then it's terminating otherwise it's not.

$\frac{63}{72} \times 185=\frac{21}{24}\times 175=\frac{7}{8}\times 175$

$=\frac{7}{23}\times 175\\ =\frac{7\times 5^3}{2^3\times 5^3}\times 175\\ =\frac{875}{10^3}\times 175\\ =0.875\times 175\\=153.125$

Hence, given expression is terminating.