Write down the decimal expansion for 163125-

16 3125 = 2^ 4 5^ 4 × 5 #160; int o desimal form ⇒ Multiply and divide by 2 ⇒ 2^ 4 × 2 5^ 4 × 5× 2 =( 2 5 #160; ) ^ 4 · ...

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Standard VII

Mathematics

Writing Rational Numbers as Decimals

Write down th...

Question

Write down the decimal expansion for $\frac{16}{3125}$ .

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Solution

$\begin{matrix} \frac{16}{3125} = \frac{2^{4}}{5^{4} \times 5} i n t o d e s i m a l f o r m \Rightarrow M u l t i p l y a n d d i v i d e b y 2 \Rightarrow \frac{2^{4} \times 2}{5^{4} \times 5 \times 2} = {(\frac{2}{5})}^{4} \cdot \frac{2}{10} = 0.2 \times {(0.4)}^{4} = 0.00512 \end{matrix}$

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Similar questions

Q. Write down the decimal expansions of
(i)

\frac{13}{3125}

(ii)

\frac{17}{8}

(iii)

\frac{15}{1600}

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Question 2
Write down the decimal expansions of
(i) $\frac{13}{3125}$
(ii) $\frac{17}{8}$
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(i)

\frac{13}{3125}

(ii)

\frac{17}{8}

(iii)

\frac{15}{1600}

(iv)

\frac{23}{2^{3} 5^{2}}

(v)

\frac{6}{15}

(vi)

\frac{35}{50}

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Write down the decimal expansion for 163125.

163125=2454×5intodesimalform⇒Multiplyanddivideby2⇒24×254×5×2=(25)4⋅210=0.2×(0.4)4=0.00512

Write down the decimal expansion for $\frac{16}{3125}$ .

$\begin{matrix} \frac{16}{3125} = \frac{2^{4}}{5^{4} \times 5} i n t o d e s i m a l f o r m \Rightarrow M u l t i p l y a n d d i v i d e b y 2 \Rightarrow \frac{2^{4} \times 2}{5^{4} \times 5 \times 2} = {(\frac{2}{5})}^{4} \cdot \frac{2}{10} = 0.2 \times {(0.4)}^{4} = 0.00512 \end{matrix}$