🔢(Tips, Tricks & Shortcuts) – Computation of Whole Numbers & Decimals

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✅ PART A: COMPUTATION OF WHOLE NUMBERS

🔹 1. BODMAS Rule (SSC Favourite Trap)

Always follow:
Bracket → Of → Division → Multiplication → Addition → Subtraction

Shortcut Tip:
Division & multiplication → Left to Right
Addition & subtraction → Left to Right

Example:
36 ÷ 6 × 3 =
→ 6 × 3 = 18 (❌ not 36 ÷ 18)

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🔹 2. Divisibility Rules (Must Memorize)

Number	Shortcut
2	Last digit even
3	Sum of digits divisible by 3
4	Last 2 digits divisible by 4
5	Ends with 0 or 5
6	Divisible by 2 & 3
8	Last 3 digits divisible by 8
9	Sum of digits divisible by 9
11	(Odd place sum − Even place sum) multiple of 11

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🔹 3. Unit Digit Trick (Very Common in SSC)

Only multiply unit digits.

Example:
Find unit digit of $17^{23} × 9^{45}$

• 7²³ → cycle: 7,9,3,1 → 23 ÷ 4 → remainder 3 → 3

• 9⁴⁵ → cycle: 9,1 → odd → 9

Unit digit → 3 × 9 = 7

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🔹 4. Squares & Cubes (Quick Recall)

Squares (1–30) & cubes (1–20) are mandatory.

Examples:

• 15² = 225

• 25² = 625

• 35² = 1225

👉 Ending with 5 trick:
(45)² = 4×5 | 25 = 2025

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🔹 5. LCM–HCF Shortcut

LCM × HCF = Product of numbers

Example:
If HCF = 12, numbers = 12 & 60
LCM = (12×60)/12 = 60

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✅ PART B: COMPUTATION OF DECIMALS

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🔹 6. Decimal × 10, 100, 1000

Just shift decimal point.

• ×10 → right 1 place

• ×100 → right 2 places

• ÷1000 → left 3 places

Example:
0.045 × 1000 = 45

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🔹 7. Decimal to Fraction (Instant Method)

Decimal	Fraction
0.5	1/2
0.25	1/4
0.75	3/4
0.2	1/5
0.125	1/8
0.375	3/8

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🔹 8. Multiplying Decimals (No Confusion Rule)

Step 1: Multiply normally (ignore decimal)
Step 2: Count total decimal places

Example:
0.24 × 0.5
→ 24 × 5 = 120
Decimal places = 3
Answer = 0.120 = 0.12

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🔹 9. Division of Decimals Shortcut

Make divisor whole number.

Example:
4.5 ÷ 0.15
Multiply both by 100
→ 450 ÷ 15 = 30

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🔹 10. Approximation Trick (Very Useful)

SSC allows approximate answers.

Example:
19.98 × 5.02 ≈ 20 × 5 = 100

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🔹 11. Recurring Decimal Shortcut

0.333… = 1/3
0.666… = 2/3
0.999… = 1

For two repeating digits:
0.2727… = 27/99 = 3/11

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🔹 12. Decimal Comparison Shortcut

Compare digit by digit (no conversion needed).

Example:
0.4567 vs 0.459
→ 4567 vs 4590 → 0.459 bigger