Ex 2.6 Q5 Fractions-and-Decimals-Solutions NCERT Maths Class 7

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Question

 Find:

i) \(2.5 × 0.3  \) 

ii) \(\rm{}0.1 × 51.7  \) 

iii) \(\rm{}0.2 × 316.8 \)

iv) \(\rm{}1.3 × \rm{}3.1\)

v) \(\rm{}0.5 ×0.05  \)

vi) \(\rm{}11.2 × 0.15\)

vii) \(\rm{}1.07× 0.02 \) 

viii) \(\rm{}10.05 × 1.05 \)

ix) \(\rm{}101.01× 0.01 \)

 x) \(\rm{}100.01 × 1.1 \)

Text Solution

What is known?

Decimal numbers.

 What is unknown?

Product of these two numbers.

 Reasoning:

Covert decimal number into fraction and then find the product.

Steps:

i) \(2.5 × 0.3  \) 

\[\begin{align}&= \frac{{25}}{{10}} \times \frac{3}{{10}} \hfill \\\,\,\, &= \frac{{25 \times 3}}{{100}} \hfill \\\,\,\, &= \frac{{75}}{{100}} \hfill \\\,\,\, &= 0.75 \hfill \\\hfill \\\end{align}\] 

ii) \(\rm{}0.1 × 51.7  \) 

\[\begin{align}&= \frac{1}{{10}} \times \frac{{517}}{{10}} \hfill \\\,\,\, &= \frac{{1 \times 517}}{{100}} \hfill \\\,\,\, &= \frac{{517}}{{100}} \hfill \\\,\,\, &= 5.17 \hfill \\\end{align}\]

iii) \(\rm{}0.2 × 316.8 \)

\[\begin{align}&= \frac{2}{{10}} \times \frac{{3168}}{{10}} \hfill \\\,\,\,\,\, &= \frac{{2 \times 3168}}{{100}} \hfill \\\,\,\,\,\, &= \frac{{6336}}{{100}} \hfill \\\,\,\,\,\, &= 63.36 \hfill \\\end{align}\]

iv) \(\rm{}1.3 × \rm{}3.1\)

\[\begin{align}&= \frac{{13}}{{10}} \times \frac{{31}}{{10}} \hfill \\\,\,\,\,\,\,\, &= \frac{{13 \times 31}}{{100}} \hfill \\\,\,\,\,\,\,\, &= \frac{{403}}{{100}} \hfill \\\,\,\,\,\,\,\, &= 4.03 \hfill \\\end{align}\]

v) \(\rm{}0.5 ×0.05  \)

\[\begin{align}&= \frac{5}{{10}} \times \frac{5}{{100}} \hfill \\\,\,\,\, &= \frac{{5 \times 5}}{{1000}} \hfill \\\,\,\, &= \frac{{25}}{{1000}} \hfill \\\,\, &= 0.025 \hfill \\\hfill \\\end{align}\]

vi) \(\rm{}11.2 × 0.15\)

\[\begin{align}&= \frac{{112}}{{10}} \times \frac{{15}}{{100}} \hfill \\\,\,\,\,\, &= \frac{{112 \times 15}}{{1000}} \hfill \\\,\,\,\, &= \frac{{1680}}{{1000}} \hfill \\\,\,\, &= 1.68 \hfill \\\end{align}\]

vii) \(\rm{}1.07× 0.02 \) 

\[\begin{align}&= \frac{{107}}{{100}} \times \frac{2}{{100}} \hfill \\\,\,\,\,\,\, &= \frac{{107 \times 2}}{{10000}} \hfill \\\,\,\,\,\, &= \frac{{214}}{{10000}} \hfill \\\,\,\,\,\, &= 0.0214 \hfill \\\end{align}\]

viii) \(\rm{}10.05 × 1.05 \)

\[\begin{align}&= \frac{{1005}}{{100}} \times \frac{{105}}{{100}} \\{}& = \frac{{1005 \times 105}}{{10000}} \\{}& = \frac{{105525}}{{10000}} \\{}& = 10.5525 \\\end{align}\]

ix) \(\rm{}101.01× 0.01 \)

\[\begin{align}& = \frac{{10101}}{{100}} \times \frac{1}{{100}} \\{}& = \frac{{10101 \times 1}}{{10000}} \\{}& = \frac{{10101}}{{10000}} \\{}& = 1.0101 \\\end{align}\]

 x) \(\rm{}100.01 × 1.1 \)

\[\begin{align}& = \frac{{10001}}{{100}} \times \frac{{11}}{{10}} \\{}& = \frac{{10001 \times 11}}{{1000}} \\{}& = \frac{{110011}}{{1000}} \\{}& = 110.011 \\\end{align}\]

  
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