Converting - fractions ↔ decimals ↔ percentages

1.1.16 · Maths › Arithmetic & Number Systems

Teen forms aur unka "matlab"

Ek hi fact jo sab kuch clear kar deta hai: $p % = \frac{p}{100}$

YE MASTER KEY KYUN HAI: Symbol " $%$ " bas " $\div 100$ " ka shorthand hai. Jaise hi aap $%$ ko $\div 100$ se replace karte ho, ek percentage fraction ban jaata hai, jise phir decimal mein convert kar sakte ho. Neeche har conversion isi ek idea se bani hai.

Figure — Converting - fractions ↔ decimals ↔ percentages

Har conversion ko first principles se derive karna

1. Fraction → Decimal

Ek fraction $\frac{a}{b}$ hai hi division $a \div b$ . To bas long division karo.

KYUN: $\frac{3}{4}$ ka literally matlab hai "3 ko 4 barabar shares mein divide karo". Division definition hai, koi trick nahi.

$\frac{3}{4} = 3 \div 4 = 0.75$

2. Decimal → Fraction

Last digit ki place value padho aur use 10 ki corresponding power ke upar rakho, phir simplify karo.

KYUN: $0.75$ ka matlab hai "7 tenths + 5 hundredths" $= \frac{75}{100}$ . Last digit hundredths place mein hai $\Rightarrow$ denominator $100$ . $0.75 = \frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4}$

3. Decimal → Percentage

Kyunki $p % = \frac{p}{100}$ , $p$ find karne ke liye hum poochte hain "ye decimal kitne hundredths hai?" — 100 se multiply karo. $decimal \times 100 = percent$ KYUN: $0.75 = \frac{75}{100} = 75%$ . 100 se multiply karne se hundredths ki count milti hai, jo exactly wahi hai jo "percent" chahta hai.

4. Percentage → Decimal

Upar wala ulta karo: 100 se divide karo (yani $%$ ko $\div 100$ se replace karo). $75% = \frac{75}{100} = 0.75$

5. Fraction → Percentage

Combine karo: fraction ko decimal mein badlo, phir $\times 100$ . Ya seedha denominator ko 100 tak scale karo. $\frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100} = 75%$

6. Percentage → Fraction

$p % = \frac{p}{100}$ , phir simplify karo. $40% = \frac{40}{100} = \frac{2}{5}$

Worked examples

Common mistakes (steel-manned)

Recall Feynman: ek 12-saal ke bachche ko explain karo

Ek chocolate bar socho. Agar use 4 barabar tukdon mein todo aur 3 khao, to ye fraction $\frac{3}{4}$ hai. Agar socho bar 100 tiny squares mein kata hua hai, to tumne 75 khaaye hoge — ye percentage hai, $75%$ , kyunki "percent" ka matlab bas "100 mein se" hota hai. Aur agar calculator wale tarike se likho, $3 \div 4 = 0.75$ — ye decimal hai. Utni hi chocolate, teen alag tarike se boli! Swap karne ke liye: divide karna decimal deta hai, aur " $\times 100$ ya $\div 100$ " tumhe "100-mein-se" duniya mein le jaata ya wapas laata hai.

Quick reference table

Fraction	Decimal	Percent
$\frac{1}{2}$	$0.5$	$50%$
$\frac{1}{4}$	$0.25$	$25%$
$\frac{3}{4}$	$0.75$	$75%$
$\frac{1}{5}$	$0.2$	$20%$
$\frac{1}{8}$	$0.125$	$12.5%$
$\frac{1}{3}$	$0. \overline{3}$	$33 \frac{1}{3} %$
$\frac{1}{100}$	$0.01$	$1%$

80/20: Is table ki pehli chhe rows yaad karo. Ye exam ke zyaadatar conversions turant cover kar leti hain.

Flashcards

Symbol

%

ka literally kya matlab hai?

"per hundred", yani

\div 100

\frac{3}{4}

ko decimal mein convert karo.

3 \div 4 = 0.75

0.75

ko percentage mein convert karo.

0.75 \times 100 = 75%

Decimal ko percentage mein kaise badlate hain?

100 se multiply karo.

Percentage ko decimal mein kaise badlate hain?

100 se divide karo.

40%

ko lowest terms mein fraction mein convert karo.

\frac{40}{100} = \frac{2}{5}

0.7 = \frac{7}{10}

kyun hai,

\frac{7}{100}

kyun nahi?

Ek decimal place = tenths, isliye denominator 10 hai.

\frac{1}{3}

ko exact percentage mein express karo.

33 \frac{1}{3} %

(kyunki

0. \overline{3} \times 100

150%

ko decimal aur fraction mein convert karo.

1.5 = \frac{3}{2}

(percentages 100% se zyada ho sakti hain).

\frac{5}{8}

ko percentage mein convert karo.

5 \div 8 = 0.625 \Rightarrow 62.5%

Connections

Fractions - simplifying and equivalent fractions
Decimal place value
Ratio and proportion
Percentage increase and decrease
Recurring decimals to fractions
Long division