Ex 2.5 Q1 Fractions and Decimals - NCERT Maths class 7

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Question

What is greater?

i) \(0.5 \) or \(0.05\) ii) \(0.7\) or \(0.5\) iii) \(7\) or \(0.7\)
iv) \(1.37 \) or \(1.49\) v) \(2.03\) or \(2.30\) vi) \(0.8\) or \(0.88\)

 

Text Solution

What is known?

Decimal numbers

What is unknown?

Which decimal number is greater.

Reasoning:

First convert these decimals into fractions then convert them into like fraction, now we can simply find out which fraction/decimal is greater.

Steps:

(i) \(0.5 \) or \(0.05\)

\(\begin{align}0.5  \quad&\boxed{\;\;}\quad 0.05\\\\\frac{5}{10} \quad &\boxed{\;\;} \quad \frac{5}{100}\end{align}\)

Converting them into like fractions, we get

\[\begin{align}\frac{5\times 10}{10\times 10} \quad\boxed{\;\;}\quad \frac{5\times 1}{100\times 1}\\\\\frac{50}{100} \quad\boxed{\;\;}\quad \frac{50}{100}\\\\\frac{50}{100} \quad\boxed{\gt}\quad \frac{5}{100}\end{align}\]

Therefore\(,0.5 > 0.05.\)

ii) \(0.7\) or \(0.5\)

\[\begin{align}~0.7\,  \quad\boxed{\;\;}\quad 0.5\\\\\frac{7}{10}  \quad\boxed{\;\;}\quad \frac{5}{10} \\\\
\frac{7}{10}  \quad\boxed{\gt}\quad  \frac{5}{10}\end{align}\]

Therefore,\(0.7\) \(>\) \(0.5\).

iii) \( 7 \) or \(0.7\) 

\[\begin{align}\text{7} \quad\boxed{\;\;}\quad \frac{7}{10}\\\\=\frac{7\times 10}{1\times 10} \quad\boxed{\;\;}\quad \frac{7}{10}\\\\\frac{70}{10} \quad\boxed{\gt}\quad \frac{7}{10}\end{align}\]

Therefore, \(7 > 0.7.\)

\(7\) is greater.

iv) \(1.37\) or \(1.49\)

\[\begin{align}&=1\text{.37} \quad\boxed{\;\;}\quad \text{1}\text{.49}\\\\&=\frac{137}{100} \quad\boxed{\;\;}\quad \frac{149}{100}\\\\&=\frac{137}{100} \quad\boxed{\lt}\quad \frac{149}{100}\end{align}\]

Therefore, \(1.37\) \(< \)\(1.49\)

\(1.49\) is greater.

v) \(2.03\) or \(2.30\)

\[\begin{align}\text{2}\text{.03} \quad\boxed{\;\;}\quad \text{2}\text{.30} \\\\\frac{203}{100} \quad\boxed{\;\;}\quad \frac{230}{100}\\\\\frac{203}{100} \quad\boxed{\lt}\quad \frac{230}{100}\end{align}\]

Therefore, \(2.03\) \(<\) \(2.30\)

\(2.30 \) is greater.

vi) \(0.8\) or \(0.88\)

\[\begin{align}\frac{08}{10} \quad\boxed{\;\;}\quad \frac{088}{100}\end{align}\]

Converting them into like fractions, we get

\[\begin{align}\frac{8\times 10}{10\times 10} \quad\boxed{\;\;}\quad \frac{88}{100}\\\\\frac{80}{100} \quad\boxed{\lt}\quad \frac{88}{100} \end{align}\]

Therefore, \(0.8 < 0.88.\)

\(0.88\) is greater.