Ex 2.5 Q4 Fractions and Decimals - NCERT Maths class 7

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Question

Q4. Express in \(\rm{kg}\):

i) \(200\) g ii) \(3470\) g iii) \(4\,\rm{kg} \ 8\,\rm{g}\)

 

Text Solution

What is known?

Weight in grams

What is unknown?

Weight in kilograms.

Reasoning:

\(\begin{align}1\rm{g} = \frac{1}{{1000}}\rm{kg}\end{align}\)

Steps:

(i) \(200\,\rm{g}\)

 \(\because1000\,\rm{g} = 1\,\rm{kg}\)

\(\because 1\,\rm{g} = \begin{align}\frac{1}{{1000}}\end{align}\,\rm{kg}\)

 \[\begin{align} \text{So, } 200\,\rm{g} = 200 ×\frac{1}{{1000}}\,\rm{kg}\\\\=\frac{{200}}{{1000}}\,\rm{kg}\\ \\= 0.200\,\rm{kg}\end{align}\]

 or

\[\begin{align} &=\frac{{200}}{{1000}}\\\\&=\frac{2}{{10}}\\\\&= 0.2\,\rm{kg}\end{align}\]

 

(ii) \(3470\,\rm{g}\)

 \(\because 1000\,\rm{g} =1\,\rm{kg}\)

 \(\because1\,\rm{g} =\begin{align}\frac{1}{{1000}}\end{align}\,\rm{kg}\)

\[\begin{align}3470\,\rm{g}& = 3470 \times (\frac{1}{{1000}})\,\rm{kg}\\3470\,\rm{g} &= (\frac{{3470}}{{1000}})\,\rm{kg}\\3470{\,\rm{g}} &= \frac{{347}}{{100}} \\ 3470{\,\rm{g}} &= 3.47{\,\rm{kg}} \end{align}\]

(iii) \(4\,\rm{kg} \ 8\,\rm{g}\)

\[\begin{align}4\,\rm{kg} \ 8\,\rm{g} &= 4\,\rm{kg} + 8\,\rm{g}\\4\,\rm{kg} \ 8 \,\rm{g} &=4\,\rm{kg} + \frac{8}{{1000}}\,\rm{kg} \end{align}\]

\(\because 1000\,\rm{g}= 1\,\rm{kg}\)

\( \because 1\,\rm{g} = \begin{align}\frac{1}{{1000}}\end{align}\,\rm{kg}\)

\[\begin{align}4 \,\rm{kg} \ 8\,\rm{g} &= 4 \,\rm{kg} + 0.008 \,\rm{kg}\\4\,\rm{kg} \ 8\,\rm{kg}&=4.008\,\rm{kg}\end{align}\]