Percentage Conversion (Decimal / Fraction / Ratio) – SSC CGL Maths

Conversion Topics Speed Booster DI Friendly

English: Conversions make percentage questions fast—especially in DI, Profit-Loss, Discount, SI/CI.
Hinglish: SSC me speed ka main reason yehi hota hai: decimal ↔ %, fraction ↔ %, ratio ↔ % share.

1) % ⇄ Decimal (Fastest)

% → decimal: ÷100 (move decimal 2 places left)

decimal → %: ×100 (move decimal 2 places right)

Convert	Steps	Answer
25% → decimal	25 ÷ 100	0.25
7.5% → decimal	7.5 ÷ 100	0.075
0.08 → %	0.08 × 100	8%
1.2 → %	1.2 × 100	120%
0.0075 → %	0.0075 × 100	0.75%

English: “Percent point shift” = 2 places.
Hinglish: “2 zeros ka game” — bas decimal ko 2 step shift.

SSC Quick Checks (1-liners)

0.5 = 50% (half)
0.25 = 25% (quarter)
0.2 = 20% (1/5)
0.125 = 12.5% (1/8)

2) % ⇄ Fraction (Simplify Always)

% → fraction: p% = p/100 (then reduce)

fraction a/b → %: (a/b)×100

Convert	Steps	Answer
18% → fraction	18/100 = 9/50	9/50
12.5% → fraction	12.5/100 = 125/1000 = 1/8	1/8
3/20 → %	(3/20)×100 = 15	15%
3/8 → %	(3/8)×100 = 37.5	37.5%
7% → fraction	7/100	7/100

English: If denominator is 2,4,5,8,10,20,25,40,50,100 → conversion becomes instant.
Hinglish: Aise denominators me “×100” karte hi answer clean aata hai.

Extra Trick: Terminating decimal → exact fraction

English: 0.075 = 75/1000 = 3/40 (reduce).
Hinglish: jitne decimal digits, utna 10^n denominator.

0.6 = 6/10 = 3/5

0.125 = 125/1000 = 1/8

3) Ratio ⇄ Percentage (Share & Split)

(A) Ratio a:b → % share (Part out of Total)

Total parts = a + b

A% = a/(a+b)×100, B% = b/(a+b)×100

Ratio	A%	B%	English + Hinglish
2:3	2/5×100 = 40%	3/5×100 = 60%	Total=5 parts → A gets 2 parts, B gets 3 parts
1:4	1/5×100 = 20%	4/5×100 = 80%	“1 out of 5” → 20% share
3:7	3/10×100 = 30%	7/10×100 = 70%	Easy when total is 10

(B) % → Ratio (p% and (100−p)%)

p% : (100−p)% = p : (100−p) (simplify using gcd)

Example: 40% and 60% ⇒ 40:60 = 2:3.
Hinglish: Percent ko ratio banana ho to “100−p” pair bana do.

SSC Trap Note: % share vs % increase (different)

English: Share means part/total. Increase means change/old.
Hinglish: Ratio-share me divide “total” se hota hai, increase/decrease me divide “old/base” se.

4) Most-used values (Cheat Table)

English: Memorize these. DI + Percentage becomes 2x faster.
Hinglish: Ye table yaad ho gayi to 50% calculation automatic.

Fraction	Decimal	%	Memory
1/2	0.5	50%	Half
1/3	0.333…	33.33%	One-third
2/3	0.666…	66.66%	Two-third
1/4	0.25	25%	Quarter
3/4	0.75	75%	100-25
1/5	0.2	20%	Divide by 5
2/5	0.4	40%	2×20
3/5	0.6	60%	3×20
4/5	0.8	80%	4×20
1/8	0.125	12.5%	Very common
3/8	0.375	37.5%	3×12.5
5/8	0.625	62.5%	100-37.5
7/8	0.875	87.5%	100-12.5
1/6	0.1666…	16.66%	DI approx
5/6	0.8333…	83.33%	100-16.66

Exam move: ratio/fraction ko pehle map karo, phir calculation.

5) Mini Converter (Percent / Decimal / Fraction / Ratio)

Supported inputs: 12.5%, 0.125, 1/8, 2:3
Hinglish: Ratio do to A% & B% share bhi aayega.

Show Steps (Explain)

—

Output	Value
Percent	—
Decimal	—
Fraction	—
Percent → Ratio	—
Ratio → Shares	—

Note: Repeating decimals (like 1/3) ke liye fraction output approximation ho sakta hai.

6) Practice (SSC)

English: Try without calculator. Hinglish: Table + shift trick use karo.

0.075 ko % me badlo.
18% ko fraction me simplest form me likho.
3/20 ko % me badlo.
0.6 ko fraction aur % dono me badlo.
Ratio 2:5 me first ka % share?
60% : 40% ko ratio me likho.
5/8 ko % me badlo.
125% ko decimal aur fraction me badlo.
0.0075 ko % me badlo.
37.5% ko fraction me badlo.

Show Answers

0.075×100 = 7.5%
18/100 = 9/50
(3/20)×100 = 15%
0.6 = 3/5 and 60%
2/(2+5)×100 = 28.571…% (≈28.57%)
60:40 = 3:2
5/8×100 = 62.5%
125% = 1.25 = 5/4
0.0075×100 = 0.75%
37.5% = 37.5/100 = 375/1000 = 3/8