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Class 7 Maths Chapter 3: A Peek Beyond the Point (Hinglish Notes)

Ye chapter 5 lines mein

A Peek Beyond the Point decimals ka chapter hai. Jab koi unit itni badi ho ki cheez theek se na naapi ja sake, to use 10 tenths mein, har tenth ko 10 hundredths mein, aur aage aise hi baanta jaata hai. Decimal point Indian place value system ko in hisson tak le jaata hai, isliye 7.05 ka matlab 7 units aur 5 hundredths hai. Chapter decimals padhna, badalna, number line pe dikhana, tulna karna, jodna aur ghataana sikhata hai.

Chapter 3 ka mind map: chhoti units, tenths aur hundredths, decimal place value, naap ki units, tulna, aur dhyaan se jodna-ghataana
Poora chapter ek page pe

Ye chapter kis baare mein hai?

Sonu apni maa ko ek khilauna theek karte dekhta hai. Ek screw fit nahi hota, agla ho jaata hai, jabki dono ek jaise dikhte hain. Baareek ruler pe naapne pe pata chalta hai ki dono mein ek centimetre ke kuch tenths ka farq hai. Ye chapter unit ke aise chhote hisson ke baare mein hai, aur us tareeke ke baare mein jisse hum unhe likhte hain: decimals.

Chhoti units: tenths

Sirf poore centimetres waale ruler pe screw “2 cm aur 3 cm ke beech” hi bataaya ja sakta hai. Har centimetre ko 10 barabar hisson mein baantne pe theek pata chalta hai ki wo kahan khatm hota hai: 2 cm aur un hisson mein se 7, jise 2 7/10 cm likhte hain aur two and seven-tenth centimetres padhte hain. Har hissa ek tenth hai, aur 10 tenths ek unit banaate hain, isliye 3 4/10 units lamba pencil 34 tenths, yaani 34/10 units bhi hai. Tenths mein lambaaiyon ko hisse-hisse jodkar aur ghataakar, 10 tenths ko 1 unit banaakar, hal kiya jaata hai. Aur padho tenths aur hundredths mein.

Ek hi screw teen rulers pe: 2 aur 3 cm ke beech, 2½ cm se zyaada, aur theek 2 7/10 cm
Chhoti unit, sateek lambaai

Hundredths

8 9/10 units lamba kaagaz aadha mod diya jaaye to wo 4 4/10 aur 4 5/10 ke beech khatm hota hai. Har tenth ko phir 10 mein baantne se hundredths milte hain, aur unke 100 milkar ek unit banaate hain. Ab muda kaagaz theek 4 4/10 5/100 padha jaata hai: 4 units, 4 tenths aur 5 hundredths, jo 4 units aur 45 hundredths bhi hai.

Ek tenth ke 10 hundredths: muda kaagaz 4.45 pe khatm hota hai
Tenth ko phir das mein baanto

Decimal place value aur notation

10 mein hi kyun baante? Indian place value system mein har sthaan apne daayein waale sthaan ka 10 guna hai. Units ke daayein badhte jaane pe tenths, hundredths, thousandths aadi milte hain, yahi decimal system hai (Latin decem, das, jo Sanskrit dasha se juda hai). Poora hissa kahan khatm hota hai, ye dikhane ke liye hum decimal point lagaate hain: 705 matlab 7 hundreds aur 5 ones, 70.5 matlab 7 tens aur 5 tenths, aur 7.05 matlab 7 units aur 5 hundredths. 70.5 ko seventy point five aur 0.274 ko zero point two seven four padhte hain.

Thousands se thousandths tak ke sthaan, har ek agle ka 10 guna
Har sthaan agle ka das guna
705, 70.5 aur 7.05 place value chart mein, aur unhe kaise padhte hain
Point ki jagah se farq padta hai

Roz ki units mein decimals

Naap ki units decimals se bhari hain. 1 cm = 10 mm, isliye 1 mm = 0.1 cm aur 56 mm = 5.6 cm. 1 m = 100 cm, isliye 1 cm = 0.01 m aur 15 cm = 0.15 m. 1 kg = 1000 g, isliye 1 g = 0.001 kg aur 254 g = 0.254 kg. Aur ₹1 = 100 paise, isliye 75 paise = ₹0.75. 1 g, 10 g, 100 g, 1 kg aur 10 kg ke chaawal ke dher milkar 11.111 kg ke hote hain, har sthaan mein ek digit.

Lambaai, vajan aur paison mein decimals: 1 mm = 0.1 cm, 1 g = 0.001 kg aur 1 paisa = ₹0.01
Roz ki units mein decimals

Decimals dhoondhna aur unki tulna

Number line pe 1.4, 1 aur 2 ke beech ke 10 nishaanon mein se 4tha hai, aur 1 aur 1.1 ke beech zoom karne pe 1.01, 1.02 aadi dikhte hain. Daayein sire ke zero kuch nahi badalte (0.2 = 0.20 = 0.200), par 0.02 aur 0.002 chhote hain. Tulna ke liye baayein se ek-ek sthaan ke digits dekho: 6.465, 6.456 se bada hai kyunki uska hundredths digit bada hai. Padho decimals ki tulna.

6.456 aur 6.465 ki tulna sthaan dar sthaan: hundredths ka digit faisla karta hai
Kaun bada: 6.456 ya 6.465?

Decimals jodna aur ghataana

Priya ko skirt ke liye 2.7 m kapda chahiye aur Shylaja ko kurti ke liye 3.5 m. Points ek line mein rakhkar columns mein likhne pe 2.7 + 3.5 = 6.2 m aur 3.5 − 2.7 = 0.8 m, haasil aur udhaar bilkul poori sankhyaon jaise. Pehle andaaza lagaane se galtiyan pakdi jaati hain: do decimals ka jod unke poore hisson ke jod se zyaada aur us jod plus 2 se kam hota hai. Dekho decimals jodna aur ghataana.

Decimal points ek line mein rakhkar column jod aur ghataav: 2.7 + 3.5 = 6.2, 3.5 − 2.7 = 0.8 aur 75.345 + 86.691 = 162.036
Decimal points ek line mein

Point ka dhyaan rakho

Decimal ki galtiyan mehngi pad sakti hain: 2013 mein Amsterdam ki city council ne €1.8 million ki jagah €188 million baant diye, kyunki cents ko euros samajh liya gaya, aur dawa ke 0.05 mg ko 0.5 mg padhna das guna khuraak hai. Kuch sankhyaayein sirf decimal jaisi dikhti hain: 4.5 ghante matlab 4 ghante 30 minute, 2.5 ft chauda darwaaza matlab 2 ft 6 in, aur cricket mein 5.5 overs matlab 5 overs aur 5 balls. Decimal fractions Shridharacharya jaise prachin Bharatiya ganitagyon ke kaam mein milte hain, aur point ko alag karne waale chinh ki tarah 16vi sadi se apnaaya gaya.

Decimal jaisi dikhne waali sankhyaayein: 4.5 ghante = 4:30, 2.5 ft = 2 ft 6 in, aur 5.5 overs = 5 overs aur 5 balls
Inhe dhyaan se padho

Har sawaal, Figure it Out aur paheliyon ke jawab Chapter 3 ke NCERT solutions mein hain.

Key terms (zaroori shabd)

TermMatlab
TenthUnit ke 10 barabar hisson mein se ek, jo 1/10 ya 0.1 likha jaata hai. 10 tenths milkar 1 unit banaate hain.
HundredthUnit ke 100 barabar hisson mein se ek, jo 1/100 ya 0.01 likha jaata hai. 10 hundredths milkar 1 tenth banaate hain.
ThousandthUnit ke 1000 barabar hisson mein se ek, jo 1/1000 ya 0.001 likha jaata hai. 10 thousandths milkar 1 hundredth banaate hain.
Decimal pointWo bindu jo sankhya ke poore hisse ko uske fraction waale hisse se alag karta hai, jaise 70.5 mein.
Decimal place valueHar sthaan apne daayein waale sthaan ka 10 guna hai: thousands, hundreds, tens, units, phir tenths, hundredths aur thousandths.
Decimal system10 pe tika sankhya likhne ka tareeka. Latin shabd decem ka matlab das hai, jo Sanskrit ke dasha se juda hai.
Decimal fractionAisa fraction jiska denominator 10, 100, 1000 aadi ho, jaise 7/10 ya 45/100.
Mixed numberPoori sankhya aur fraction ek saath, jaise 2 7/10, jo decimal mein 2.7 hai.
Number line zoomDo nishaanon ke beech ke gap ko 10 hisson mein baantkar decimal ko aur sateek dhoondhna, jaise 4.185 ke liye.

Is chapter ke topics

Is chapter ke NCERT solutions Chapter ke saare exercise questions, step-by-step jawab ke saath.

Practice karo

  1. Ek tenth mein kitne hundredths hote hain?

    1. (a) 100
    2. (b) 10
    3. (c) 1000
    4. (d) 1
    Jawab dekho

    Jawab: (b) 10

  2. 7 tens aur 5 tenths decimal mein kya hai?

    1. (a) 75
    2. (b) 7.5
    3. (c) 70.5
    4. (d) 7.05
    Jawab dekho

    Jawab: (c) 70.5

  3. 15 cm kitne metre hai?

    1. (a) 1.5 m
    2. (b) 0.015 m
    3. (c) 0.15 m
    4. (d) 15 m
    Jawab dekho

    Jawab: (c) 0.15 m

  4. Inme sabse bada kaunsa hai?

    1. (a) 0.2
    2. (b) 0.02
    3. (c) 0.002
    4. (d) 0.020
    Jawab dekho

    Jawab: (a) 0.2

  5. 3.5 − 2.7 kitna hai?

    1. (a) 1.2
    2. (b) 0.8
    3. (c) 0.2
    4. (d) 1.8
    Jawab dekho

    Jawab: (b) 0.8

  6. Bus dopahar ke 4.5 ghante baad pahunchti hai. Kitne baje?

    1. (a) 4:05 p.m.
    2. (b) 4:50 p.m.
    3. (c) 4:30 p.m.
    4. (d) 4:25 p.m.
    Jawab dekho

    Jawab: (c) 4:30 p.m.

Students ke sawal

Class 7 Maths Chapter 3 ke mukhya topics kya hain?

Chhoti units ki zaroorat; unit ke tenths aur hundredths; decimal place value aur decimal point; decimals padhna aur likhna; lambaai, vajan aur paison ki units mein decimals; number line pe decimals dhoondhna aur unki tulna; decimals jodna aur ghataana; aur decimal ki galtiyan, decimal jaisi dikhne waali sankhyaayein, saath mein decimal notation ka chhota itihaas.

Kya A Peek Beyond the Point nayi Ganita Prakash kitaab mein hai?

Haan. Ye Ganita Prakash, Class 7 Maths ki kitaab Part 1 (Reprint 2026-27) ka Chapter 3 hai, pages 46 se 80 tak. Ye Sonu se shuru hota hai, jo dekhta hai ki ek jaise dikhne waale do screws ki lambaai thodi alag hai.

Unit ko 10 hisson mein hi kyun baante, 4 ya 8 mein kyun nahi?

Unit ko kitne bhi barabar hisson mein baanta ja sakta hai, par 10 Indian place value system se mel khaata hai, jisme har sthaan agle ka 10 guna hai. Unit ko tenths, hundredths aur thousandths mein baantna bas yahi pattern units ke daayein tak le jaata hai, isliye in hisson ko likhne ke liye sirf decimal point chahiye.

Kya 0.2 aur 0.20 ek hi hain?

Haan. Dono ka matlab 2 tenths hai: 0.20 matlab 2 tenths aur 0 hundredths. Decimal ke daayein sire pe zero lagaane se uski value nahi badalti. Par point aur digit ke beech ka zero value badalta hai: 0.02 matlab 2 hundredths, jo 0.2 se das guna chhota hai.

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