# Ex 2.5 Q3 Fractions and Decimals - NCERT Maths class 7

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## Question

i) Express $$5\,\rm{cm}$$ in meter and kilometer

ii) Express $$35\,\rm{mm}$$ in $$\,\rm{cm}$$,$$\,\rm{m}$$ and $$\,\rm{km}$$.

Video Solution
Fractions And Decimals
Ex 2.5 | Question 3

## Text Solution

What is known?

Lengths in centimeter and millimeter

What is unknown?

Length in different units.

Reasoning:

\begin{align}1\, \rm{cm} =\frac{1}{{100}}\rm{m}\end{align}

\begin{align}1\rm{m} = \frac{1}{{1000}}\,\rm{km}\end{align}

\begin{align}1\rm{mm} = \frac{1}{{10}}\rm{cm}\end{align}

Steps:

(i) $$5\,\rm{cm}$$

$$\because100\,\rm{cm}$$ $$=$$$$1\,\rm{m}$$

$$\therefore1\,\rm{cm}$$ $$=$$\begin{align}\frac{1}{{100}}\end{align}m

$$5\,\rm{cm}$$  $$=$$ $$5$$ $$×$$  \begin{align}\frac{{1}}{100}\rm{m}\end{align}

$$5\,\rm{cm}$$ $$=$$ $$0.05\,\rm{m}$$

Also, $$\because1000\,\rm{m}$$ $$=$$ $$1\,\rm{km}$$

$$\because1\,\rm{m}$$ $$=$$ \begin{align}\frac{1}{{1000}}\end{align}$$\rm{km}$$

Thus, $$0.05\,\rm{m}$$ $$=$$ $$0.05$$ $$×$$ \begin{align}\frac{1}{{1000}}\end{align}$$\rm{km}$$

\begin{align} & = \frac{{0.05}}{{1000}}{\text{km}} \\ & = 0.00005{\text{km}}\end{align}

(ii) Express $$35\,\rm{mm}$$ in $$\rm{cm}$$,$$\rm{m}$$ and $$\rm{km}$$.

$$\because10\,\rm{mm}$$ $$=$$ $$1\,\rm{cm}$$

$$\because1\,\rm{mm}$$ $$=$$ \begin{align}\frac{1}{{10}}\end{align} $$\rm{cm}$$

\begin{align}35{\text{mm}} &= 35 \times \frac{1}{{10}}{\text{cm}} \\ 35{\text{mm}} &= \frac{{35}}{{10}}{\text{cm}} \\ 35{\text{mm}} &= 3.5{\text{cm}} \end{align}

Now, converting $$3.5\,\rm{cm}$$ in $$\rm{m}$$, we get

$$\because100\,\rm{cm} = 1 \,\rm{m}$$

\because 1\,\rm{cm} = \begin{align}\frac{1}{{100}}\end{align}\rm{m}

3.5\,\rm{cm} = 3.5 × \begin{align}\frac{1}{{100}}\end{align}\,\rm{m}

\begin{align} 3.5{\text{cm}} &= \frac{{3.5}}{{100}}{\text{m}} \\ 3.5{\text{cm}} &= 0.035{\text{m}} \end{align}

Again, converting $$0.035\,\rm{m}$$ into $$\rm{km}$$

$$\because1000\,\rm{m}$$ $$=$$ $$1\,\rm{km}$$

\because 1\,\rm{m} = \begin{align}\frac{1}{{1000}}\end{align}\,\rm{km}

0.035\,\rm{m} = 0.035 × \begin{align}\frac{1}{{1000}}\end{align}\,\rm{km}

0.035 \,\rm{m} = \begin{align}\frac{{0.035}}{{1000}}\end{align}\,\rm{km}

$$0.035\,\rm{m} = 0.000035\,\rm{km}$$

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