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 \(\,\rm{km}\).

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 \(\rm{km}\)

 \(\because1000\,\rm{m}\) \(=\) \(1\,\rm{km}\)

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

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

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

\(0.035\,\rm{m} = 0.000035\,\rm{km} \)