WHY line up the point? Because you may only add digits that carry the same weight
(tenths to tenths, hundredths to hundredths). Adding a tenth to a hundredth is like adding
apples to oranges.
Recall Where does the decimal point go after multiplying?
The product has as many decimal places as the sum of the decimal places of the two factors.
Recall Why can we multiply divisor and dividend by 100 in division?
Because ba=100b100a — scaling top and bottom equally leaves the value unchanged; it only removes the point from the divisor.
Recall Feynman: explain to a 12-year-old
A decimal is money split past the rupee — tenths are like 10-paise coins, hundredths like paise.
To add money, you line up rupees with rupees and paise with paise, then add each pile.
To multiply, forget the point, multiply the plain numbers, and afterwards slide the point back
in — as many hops as both numbers had after their dots combined. To divide, make the number
you're dividing by into a whole number by moving both points the same amount, then share out.
Dekho, decimal koi alag cheez nahi hai — ye sirf ek fraction hai jiska denominator 10, 100, 1000
hota hai. Jaise 2.35=100235. Jab tum ye "chhupa hua fraction" dekh lete ho, to chaaron
operations ke rules apne aap samajh aa jaate hain. Point ke left me rupaye, right me paise wali soch
rakho.
Jodna/Ghatana (add/subtract): yaha sabse important baat — decimal point ko point ke neeche
line-up karo, last digit ko nahi. Zaroorat pade to zero laga do (12.4 ko 12.40 bana lo) taaki dono ke
place values match karein. Phir normal number ki tarah jodo/ghatao, point seedha neeche gir jaayega.
Guna (multiply): point ko bhool jao, plain numbers multiply karo. Phir ginto ki dono numbers me
milakar kitne decimal places the (add karo), utne places answer me daal do. Jaise 1.2 me 1 place,
0.05 me 2 place, total 3 — isliye 12×5=60 ka answer 0.060=0.06.
Bhaag (divide): jis number se divide kar rahe ho (divisor) usme jitne decimal places hain, utne
se dono — divisor aur dividend — ko 10 ki power se multiply karo, taaki divisor whole number ban
jaaye. 4.5÷0.15 me dono ko 100 se guna karo → 450÷15=30. Value badalti nahi kyunki
upar-neeche same cheez se multiply kiya. Aur hamesha answer ko ulta multiply karke check karo!
