Decimals — place value, reading and writing

1.1.15 · Maths › Arithmetic & Number Systems

Decimals exist KYUN karte hain?

Decimal mein place value KYA hoti hai?

Figure — Decimals — place value, reading and writing

Place value KAISE read karein — full derivation

Chalte hain $34.256$ use karte hain.

Step 1 — Point pe split karo. Left part 34 = whole number, right part 256 = fractional part. Yeh step kyun? Point "≥ 1 amounts" ko "< 1 amounts" se alag karta hai, isliye hum dono ko unki apni place values ke saath handle karte hain.

Step 2 — Left-side places assign karo (left jaate hue ×10). $3 \to$ tens $= 3 \times 10 = 30$ ; $4 \to$ ones $= 4 \times 1 = 4$ . Kyun? Standard whole-number place value.

Step 3 — Right-side places assign karo (right jaate hue ÷10). $2 \to$ tenths $= 2 \times 0.1 = 0.2$ $5 \to$ hundredths $= 5 \times 0.01 = 0.05$ $6 \to$ thousandths $= 6 \times 0.001 = 0.006$ Kyun? Har step right pehle wale step ka one-tenth hota hai.

Step 4 — Add karo. $30 + 4 + 0.2 + 0.05 + 0.006 = 34.256 ✓$ Yeh step kyun? Confirm karta hai ki hamari place values sahi hain — unhe original number rebuild karna chahiye.

Decimal ALOUD KAISE padhen

Words se decimal KAISE LIKHEN

Trailing & leading zeros

Common mistakes (steel-manned)

Steel-man drill

Recall Point ke baad ki digit ko bada number kyun nahi padh sakte?

Kyunki un digits mein se har ek ek alag, shrinking place mein rehti hai (tenths, hundredths…). Point ke baad "256" hota hai $2 (\frac{1}{10}) + 5 (\frac{1}{100}) + 6 (\frac{1}{1000})$ , kisi ek cheez ka two-hundred-fifty-six NAHI.

Forecast-then-Verify

Recall Predict karo: "three hundred four thousandths" ko decimal mein kaise likhen?

Pehle forecast karo, phir check karo. "thousandths" → last digit 3rd place mein. $304$ thousandths $= \frac{304}{1000} = 0.304$ . ✔ (Notice karo internal 0 rakhta hai 3 ko tenths mein, 4 ko thousandths mein.)

Feynman: ek 12-saal ke bacche ko explain karo

Recall Simplify karke explain karo

Whole numbers har step left mein 10 times badhte hain: 1 → 10 → 100. Decimals har step right mein 10 times shrink hote hain: 1 → one-tenth → one-hundredth. Chhoti dot ek fence hai: uski left mein poori cheezein hain, uski right mein ek cheez ke tukde hain. Padhne ke liye, whole part kaho, "point" kaho, phir tukdon ko ek ek digit ek time mein bolte jao. Bilkul end mein zero add karna kuch nahi badalti (0.3 = 0.30), lekin beech mein zero numbers ko chhoti boxes mein dhakelta hai, isliye woh matter karta hai.

Flashcards

What is the value of the 1st place right of the decimal point?

Tenths,

\frac{1}{10} = 0.1

What is the value of the 2nd place right of the decimal point?

Hundredths,

\frac{1}{100} = 0.01

How do you read

0.07

aloud?

"Zero point zero seven"

Write "seven and five hundredths" as a decimal.

7.05

Which is larger,

0.5

0.45

0.5

(equals

0.50 > 0.45

)

0.3 = 0.30

? Why?

Yes; trailing zeros don't change value since

\frac{3}{10} = \frac{30}{100}

Expand

34.256

into place values.

30 + 4 + 0.2 + 0.05 + 0.006

Why read decimal digits individually?

Each digit sits in a different shrinking place value

Formal name for the fraction in

0.256

Two hundred fifty-six thousandths (

\frac{256}{1000}

)

What does the decimal point mark?

The end of the ones place / boundary between wholes and fractions

Connections

Place Value in Whole Numbers — decimals is wahi ÷10 pattern ko right ki taraf extend karte hain
Fractions — har decimal place ek power-of-ten fraction hai
Comparing and Ordering Decimals — left-to-right place comparison use karta hai
Rounding Decimals — place names jaanna zaroori hai
Base-10 Number System — wholes aur decimals dono ke peeche master rule