English

Sauvaan Hissa aur Decimal Place Value

Class 7 Maths · Chapter 3: Point ke Aage Ek Jhalak · NCERT Ganita Prakash section 3.3–3.4

Seekho

8 9/10 unit lambi patti ko beech se moda. Wo 4 4/10 aur 4 5/10 ke beech khatm hoti hai, to aur chhote hisse chahiye: har tenth ko 10 hisson mein baanto. Ek unit mein 10 × 10 = 100 aise hisse, har ek 1/100 (one-hundredth). Mod 4 + 4/10 + 5/100 par hai, yaani 4 aur 45 hundredths.

10 hundredths = 1 tenth · 100 hundredths = 1 unit

Das hi kyun? Hamara place value system pehle se das par chalta hai: har sthaan apne daayein wale ka 10 guna (1000, 100, 10, 1). Daayein aage badhne par 1/10, 1/100, 1/1000 … milte hain. Yahi decimal system hai ("decem" Latin mein das, Sanskrit daśha jaisa).

1000 · 100 · 10 · 1 · 1/10 · 1/100 · 1/1000

Decimal point dikhaata hai whole hissa kahan khatm hota hai. 705 = 7 hundreds aur 5 ones; 70.5 = 7 tens aur 5 tenths; 7.05 = 7 units aur 5 hundredths. 70.5 ko padhte hain "seventy point five" aur 0.274 ko "zero point two seven four" ("two hundred seventy four" nahi), ank-ank.

7.05 = 7 × 1 + 0 × 1/10 + 5 × 1/100

Badalna: 234 tenths = 200/10 + 30/10 + 4/10 = 20 + 3 + 4/10 = 23.4. Aur 234 hundredths = 2.34; 105 tenths = 10.5. Hundredths ka jod whole numbers jaisa: 15.34 + 2.68: 4 + 8 = 12 hundredths = 1 tenth aur 2 hundredths, haasil 1 → 18.02.

234 tenths = 23.4 · 234 hundredths = 2.34

Explore: number line par hundredths.

  1. Marker ko mod par rakho: 4 aur 45 hundredths.
  2. Marker ko 4.48 par rakho.
  3. Marker ko 4 + 4/10 + 2/100 par rakho.

Yaad rakho

  • Har sthaan apne daayein wale ka 10 guna: … 10, 1, 1/10, 1/100, 1/1000.
  • Decimal point whole hissa alag karta hai: 7.05 = 7 units aur 5 hundredths; point ke baad ank ek-ek karke padho.

Quick check

7 units aur 5 hundredths kaise likhenge?

  1. 7.05
  2. 7.5
  3. 70.5
  4. 7.005
Answer

7.05. Tenths ka sthaan khaali → 0; hundredths → 5.

Socho

Kya 4 aur 2 tenths ko "42" likh sakte hain, tenths chhodkar? Kya gadbad hogi?

Ek answer

Nahi: 42 ka matlab pehle se 4 tens aur 2 ones hai. Bina point ke pata nahi chalta whole hissa kahan khatm hua, isliye 4.2 likhte hain.

Practice

Teen levels (easy, medium, hard) ke naye sawaalon se practice karo, kuch hands-on, hints aur hal ke saath. Topic poora karne ke liye pichhle 5 mein se 4 sahi karo.