1.1.17
Ek decimal bas ek fraction hota hai jiska denominator 10 ki power hoti hai . Toh 2.35 = 100 235 dekh lete ho woh hidden fraction, toh + , − , × , ÷ dhyan rakhna ki decimal point kahan jaata hai .
Har digit ek column mein baithti hai jo 10 ki power worth hai. Point ke left mein powers ≥ 0 negative hoti jaati hain:
347.28 = 3 ⋅ 1 0 2 + 4 ⋅ 1 0 1 + 7 ⋅ 1 0 0 + 2 ⋅ 1 0 − 1 + 8 ⋅ 1 0 − 2 decem = ten se aaya hai. Dot batata hai kahan 1 0 0
Point ko line up kyon karein? Kyunki aap sirf unhi digits ko add kar sakte ho jo same weight carry karti hain
(tenths ko tenths se, hundredths ko hundredths se). Ek tenth ko ek hundredth se add karna waisa hi hai jaise
apples ko oranges se add karna.
12.4 + 3.75 Step 1 Pad karo: 12.40 + 3.75 Kyon? Dono 100 ⋅ 100 1240 + 100 375 Step 2 Whole numbers add karo: 1240 + 375 = 1615 Kyon? Same denominator ⇒ numerators add karo.
Step 3 100 100 1615 = 16.15 Kyon? Point aligned points ke neeche seedha jaata hai.
✅ Answer 16.15
8.3 − 5.47 Step 1 Pad karo: 8.30 − 5.47 100 830 − 100 547 Kyon? Place value barabar karo.
Step 2 Subtract karo: 830 − 547 = 283 Kyon? Common denominator ke upar numerators.
Step 3 100 283 = 2.83
Intuition Places ADD kyon hote hain1 0 − m m 1 0 − n n m + n multiply hoti hai,
aur 1 0 − m ⋅ 1 0 − n = 1 0 − ( m + n ) add hote hain.
1.2 × 0.05 Step 1 Points hatao: 12 × 5 = 60 Kyon? A = 12 , B = 5 Step 2 Places count karo: 1.2 1 0.05 2 3 Step 3 Point is tarah lagao ki answer mein 3 60 → 0.060 Kyon? 1 0 3 60 0.06
4.5 ÷ 0.15 Step 1 Divisor 0.15 2 100 15 450 Kyon? Divisor ka point khatam ho jaata hai.
Step 2 Long divide karo: 450 ÷ 15 = 30 Inverse se check karo: 30 × 0.15 = 4.5
2.4 ÷ 4 Step 1 Divisor pehle se whole hai. Divide karo, point ko apni jagah ke upar rakhte hue: 24 ÷ 4 = 6 2.4 ÷ 4 = 0.6 Step 2 Verify karo: 0.6 × 4 = 2.4
Common mistake Add karte waqt "LAST digits line up karo"Kyon sahi lagta hai: whole numbers mein aap hamesha right-align karte ho, toh yahi aadat aati hai.
Trap: 12.4 + 3.75 4 5 Fix: decimal points align karo, last digits nahi. Pehle zeros se pad karo.
Common mistake "Adding/subtracting mein bhi places count karo"Kyon sahi lagta hai: aapne abhi multiplication ke liye places count karna seekha.
Trap: aap places sirf multiplication ke liye add karte ho. + , − Fix: yaad rakho — count-and-add sirf multiply-only move hai.
Common mistake Divide karte waqt sirf EK number mein point shift karnaKyon sahi lagta hai: aap jaante ho divisor whole banana chahiye.
Trap: 4.5 ÷ 0.15 = 4.5 ÷ 15 dono ko same 1 0 k Fix: numerator aur denominator dono ko 10 ki same power se multiply karo.
Recall Multiply karne ke baad decimal point kahan jaata hai?Product mein utne hi decimal places hote hain jitne dono factors ke decimal places ka sum ho.
Recall Division mein divisor aur dividend dono ko 100 se multiply kyon kar sakte hain?Kyunki b a = 100 b 100 a
Recall Feynman: ek 12-saal ke bachche ko explain karoEk decimal waisa paisa hai jo rupee ke baad bhi jaata hai — tenths 10-paise coins ki tarah hain, hundredths paise ki tarah.
Add karne ke liye, rupees ko rupees ke saath aur paise ko paise ke saath line up karo, phir har dheri add karo.
Multiply karne ke liye, point bhool jao, plain numbers multiply karo, aur baad mein point wapas slide karo —
utne hops jinne dono numbers ke dots ke baad combined place the. Divide karne ke liye, jis number se divide kar rahe ho
usse whole number banao dono points same amount move karke, phir baant lo.
Mnemonic Operations yaad karo"A dd/S ubtract → A lign the point. M ultiply → M ove-and-add the places.
D ivide → D itch the point in the divisor (shift both)."
Place Value and Powers of Ten Fractions to Decimals conversion Rounding and Significant Figures Long Division algorithm Scientific Notation (same "exponents add on multiply" idea)
Adding decimals: kya align karte hain? Decimal points (zeros se pad karo equal places tak).
Decimals add karne se pehle zeros se pad kyon karte hain? Dono numbers ko common denominator dene ke liye (10 ki same power) taaki like place values add hon.
Multiplying decimals: product mein kitne decimal places hote hain? Dono factors ke decimal places ka sum.
1.2 × 0.05 = ? 0.06
Decimal se divide karte waqt: pehla step kya hai? Divisor AUR dividend dono ko 10 ki same power se multiply karo taaki divisor whole number ban jaaye.
4.5 ÷ 0.15 = ? 30
Kaunsa operation "decimal places count-and-add" use karta hai? Sirf Multiplication (addition/subtraction nahi).
8.3 − 5.47 = ? 2.83
347.28 3 ⋅ 1 0 2 + 4 ⋅ 1 0 1 + 7 ⋅ 1 0 0 + 2 ⋅ 1 0 − 1 + 8 ⋅ 1 0 − 2
Division answer check karne ka quick tarika? Quotient ko divisor se multiply karo; aapko dividend wapas milna chahiye.
Fraction over power of 10
Pad to common denominator
Add or subtract whole numbers
Exponents 10^-m times 10^-n add
