"तरुण के स्वप्न" पाठ किसके उद्बोधन का अंश है?

सुभाषचंद्र बोस

"उनके स्वप्न के उत्तराधिकारी आज हम हैं" में "हम" किसके लिए है?

देश के तरुण/युवा वर्ग के लिए

नेताजी ने किस प्रकार के राष्ट्र का स्वप्न देखा था?

सर्वांगीण स्वाधीन और संपन्न राष्ट्र

नेताजी के आदर्श समाज में नारी का स्थान कैसा होगा?

पुरुष के समान अधिकार और भागीदारी

"आलसी तथा अकर्मण्य के लिए कोई स्थान नहीं रहेगा" — क्यों कहा गया?

क्योंकि नेताजी श्रम और कर्म की मर्यादा वाले समाज की कल्पना करते थे

Express \(\dfrac{3}{4}\) as a percentage.

Scale to denominator \(100\): \(\dfrac{3}{4} = \dfrac{75}{100} = 75\%\).

How do you turn any fraction into a percentage?

Multiply it by \(100\), or find an equivalent fraction with denominator \(100\).

What is \(50\%\) of a quantity \(s\)?

It is \(\dfrac{50}{100} \times s = \dfrac{1}{2}s\).

Convert \(20\%\) to a fraction in simplest form.

\(\dfrac{20}{100} = \dfrac{1}{5}\).

Where does the word per cent come from?

From the Latin per centum, meaning by the hundred or out of a hundred.

Express \(\dfrac{1}{5}\) as a percentage.

\(\dfrac{1}{5} = \dfrac{20}{100} = 20\%\).

Why are percentages useful for comparison?

They place all proportions on a common base of \(100\), so totals of different sizes can be compared.

Convert \(0.45\) to a percentage.

Multiply by \(100\): \(0.45 = 45\%\).

What percentage is \(\dfrac{30}{40}\)?

It equals \(\dfrac{75}{100} = 75\%\).

Fractions in Disguise

Q: What does the symbol \(\%\) mean?

It means per cent, or out of every hundred, so \(25\%\) is \(25\) out of \(100\).

Class 8 Mathematics · Ganita Prakash Part 2 · Chapter 1

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Summary

This chapter reveals percentages as fractions in disguise. The word per cent comes from the Latin per centum, meaning out of a hundred, so a percentage is simply a fraction with denominator \(100\): \(25\% = \dfrac{25}{100}\). Any fraction can be expressed as a percentage by finding an equivalent fraction with denominator \(100\), for example \(\dfrac{3}{4} = \dfrac{75}{100} = 75\%\), or by multiplying the fraction by \(100\). Conversely, a percentage is converted back to a fraction or decimal by dividing by \(100\). The chapter shows how percentages let us compare proportions on a common scale even when the underlying totals differ, which is exactly why they are so widely used in marks, discounts and statistics. Finding a percentage of a quantity means taking that fraction of it, so \(50\%\) of \(s\) is \(\dfrac{1}{2}s\). These tools connect fractions, decimals and percentages into a single flexible language for describing parts of a whole.

Percentages as fractionsExpressing fractions as percentagesConverting between fractions, decimals and percentagesFinding a percentage of a quantityComparing proportions

Key terms

Per cent

A fraction with denominator \(100\); the symbol \(\%\) means out of every hundred.

Percentage

A way of writing a proportion as parts per hundred, e.g. \(33\% = \dfrac{33}{100}\).

Equivalent fraction

A fraction of equal value with a different denominator, used to reach denominator \(100\).

Fraction-to-percent

Multiplying a fraction by \(100\) (or scaling its denominator to \(100\)) to express it as a percentage.

Percent of a quantity

Taking that fraction of the quantity; \(p\%\) of \(s\) equals \(\dfrac{p}{100} \times s\).

Common scale

The benefit of percentages: proportions from different totals can be compared on a base of \(100\).

Extra questions & answers

Try one from this chapter

What does the symbol \(\%\) mean?

Flashcards & interactive practice

Fractions in Disguise

CBSE Class 8 community

Summary

Key terms

Extra questions & answers

Practice quiz · Fractions in Disguise

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