Question

Write rationals in decimal form using Theorem 1.4
1) 3650/5^3​

Answer 1

$Given \: Rational \:number \: \frac{3650}{5^{3}}$

$= \frac{ 5 \times 5\times 146 }{ 5\times 5 \times 5 } \\= \frac{146}{5} \\= \frac{146 \times 2 }{ 5 \times 2 }\\ \blue{ (Denominator \: is \: of \:the \: form \: 2^{n} \times 5^{m} )} \\= \frac{ 292 }{10} \\= 29.2 \: \blue{ ( Terminating \: decimal )}$

Therefore.,

$\red{ Rational \:number \: \frac{3650}{5^{3}}}$

$\green { = 29.2}$

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