Class 7 Maths · Chapter 3
Short answer: Class 7 Ganita Prakash ka Chapter 3 "A Peek Beyond the Point" decimals ki duniya khol deta hai — jahan point (decimal point) ke bayen taraf sirf whole numbers nahi, balki uske "peek beyond" karke tenths, hundredths, thousandths tak ka fine-grained number system dikhta hai. Ye chapter Large Numbers Around Us se aage badhkar batata hai ki bade numbers ke saath-saath chhote, precise fractions bhi zaroori hain — jaise 0.001 km ek meter hota hai, ya 98.6°F body temperature. NCERT Class 7 Maths Ganita Prakash chapter wise solutions dhoondh rahe students ke liye ye chapter decimal place value, comparison, aur real-life measurement (length, weight, money) ka strong base banata hai.
Chapter 3 "A Peek Beyond the Point" — naam hi sab kuch keh deta hai. Point yaani decimal point ke "beyond" jaake dekhna, jahan whole numbers khatam hote hain wahan se numbers ki ek nayi duniya shuru hoti hai — tenths (10 me se ek bhaag), hundredths (100 me se ek bhaag), aur thousandths (1000 me se ek bhaag). Class 7 Ganita Prakash ki ye tisri chapter Class 6 me decimals ke basic introduction ko aage le jaake unhe measurement, money, aur everyday precision ke context me deeply explore karti hai.
Ye chapter khud me standalone hai lekin practically ye chapter 1 "Large Numbers Around Us" ka natural extension hai — jahan bade numbers dekhe the, wahan yahan bahut chhote, precise fractions dekhte hain. Real life me — jaise petrol pump pe 2.5 litre petrol daalna, ya dukaan pe ₹49.75 ka bill, ya body temperature 98.6°F check karna — ye sab decimal numbers ke practical use hain jo is chapter me systematically cover kiye jaate hain.
Students jo NCERT Class 7 Maths Ganita Prakash chapter wise solutions search kar rahe hain unke liye ye page decimal place value se lekar comparison, addition-subtraction of decimals, aur unit conversion (km to m, kg to g, rupee to paise) tak — sab kuch step-by-step, clear working ke saath cover karta hai.
Chapter 3 Summary — 5 Minute Revision
A Peek Beyond the Point chapter ka core idea ye hai ki decimal point ke baad ki jagah bhi place value system follow karti hai — bas ab hum 1 se chhote fractions ki baat kar rahe hain. Pehla digit point ke baad tenths (1/10), doosra hundredths (1/100), teesra thousandths (1/1000) represent karta hai.
Chapter me ye topics cover hote hain: decimal numbers ko expand karna aur place value likhna, decimals ko number line pe represent karna, do decimals ko compare karna (jaise 3.45 aur 3.5 me bada kaun), decimals ka addition aur subtraction, aur real-world measurement problems — length (km-m-cm), weight (kg-g), capacity (litre-ml), aur money (rupees-paise) — jinme decimal ka use hota hai.
Ek important skill jo bar-bar test hoti hai: decimals compare karte waqt digits ki length nahi, place value dekhni chahiye — 3.5 aur 3.45 me 3.5 bada hai kyunki 3.5 = 3.50, aur 50 hundredths > 45 hundredths. Ye common mistake exercises me bahut common hai.
In-Text Questions — Solutions
Figure it out (Section 3.1): Likho ki 25.7 me digit 7 ka place value kya hai?
25.7 me decimal point ke turant baad wala digit tenths place pe hota hai.
7 ka place value = 7 × (1/10) = 0.7
Isliye 25.7 = 2 dahai (tens) + 5 ikai (ones) + 7 tenths = 20 + 5 + 0.7
3.45 aur 3.5 me se bada number kaun sa hai — samjhao.
Dono numbers ko same number of decimal places tak likhte hain taaki compare karna asaan ho:
3.5 = 3.50
Ab tenths place compare karo: dono me 5 hai (same). Ab hundredths place compare karo: 3.50 me 0 hai, 3.45 me 5 hai.
Kyunki 0 < 5, isliye 3.50 > 3.45, matlab 3.5 bada hai.
Common galti: log sochte hain 3.45 bada hai kyunki usme zyada digits hain — ye galat hai. Digits ki ginti nahi, place value dekhni hai.
0.6 aur 0.60 — kya ye dono same hain? Samjhao.
Haan, 0.6 aur 0.60 numerically same hain.
0.6 = 6/10 = 60/100 = 0.60
Ek trailing zero (decimal point ke baad, sabse right me) add karne se number ki value change nahi hoti — bas woh usi fraction ko doosre form me likh raha hai (jaise 6/10 = 60/100).
2.375 ko expanded form me likho.
2.375 me har digit ka place value nikaalte hain:
2.375 = 2 ones + 3 tenths + 7 hundredths + 5 thousandths
2.375 = 2 + 0.3 + 0.07 + 0.005
2.375 = 2 + 3/10 + 7/100 + 5/1000
Exercise Questions — Solutions (Q1–Q6)
12.6 ko 12.60 aur 12.600 ke roop me likhne se value change hoti hai kya? Reason do.
Nahi, value change nahi hoti.
Trailing zeros (decimal point ke baad right side me add kiye gaye zeros) number ki value nahi badalte, sirf usko express karne ka tarika change karte hain.
12.6 = 12.60 = 12.600
Reason: 12.6 = 12 + 6/10. Ise 100ths me likhein: 6/10 = 60/100, isliye 12.60 = 12 + 60/100 — same value. Isi tarah 1000ths me 12.600 = 12 + 600/1000 = 12 + 6/10 — same value.
In numbers ko chote se bade order me lagao: 5.05, 5.5, 5.055, 5.505
Sabko 3 decimal places tak likhte hain compare karne ke liye:
5.05 = 5.050
5.5 = 5.500
5.055 = 5.055
5.505 = 5.505
Ab compare: 5.050 < 5.055 < 5.500 < 5.505
Ascending order: 5.05 < 5.055 < 5.5 < 5.505
Ek dukaan me pen ka daam ₹15.75 hai aur pencil ka daam ₹6.50 hai. Dono milakar kitne ka hua?
Decimals ko add karte waqt decimal points ko align karna zaroori hai (place value ke hisaab se).
15.75
+ 6.50
--------
22.25
Total = ₹22.25
Ek daudne wale ne 100 m race 12.8 second me poori ki, doosre ne 12.65 second me. Kaun tez daudta hai aur kitne second se?
Kam time = tez speed. Compare karte hain:
12.8 = 12.80
12.80 aur 12.65 compare karein: tenths place me 8 > 6, isliye 12.65 chota hai.
Doosra daudne wala tez hai (12.65 second).
Difference nikaalte hain:
12.80
− 12.65
---------
0.15
Doosra daudne wala 0.15 second se tez hai.
3 km 250 m ko decimal form me km me likho. Fir 5.6 km ko km-m form me likho.
Part 1: 1 km = 1000 m, isliye 250 m ko km me convert karte hain:
250 m = 250/1000 km = 0.250 km
3 km 250 m = 3.250 km = 3.25 km
Part 2: 5.6 km ko km aur m me todhte hain — 0.6 km ko m me convert karte hain:
0.6 km = 0.6 × 1000 m = 600 m
5.6 km = 5 km 600 m
Ek chart me ek plant ki height Monday ko 8.4 cm aur Friday ko 9.15 cm record ki gayi. Chaar din me kitni growth hui?
Subtraction karte hain, decimal places align karke (missing places me 0 add karke):
9.15
− 8.40
---------
0.75
Growth = 0.75 cm (4 din me)
Important Equations — Ek Nazar Me
| Concept | Rule / Formula |
|---|---|
| Decimal place value (tenths) | Point ke baad 1st digit = digit × 1/10 |
| Decimal place value (hundredths) | Point ke baad 2nd digit = digit × 1/100 |
| Decimal place value (thousandths) | Point ke baad 3rd digit = digit × 1/1000 |
| Comparing decimals | Same number of decimal places tak likho (trailing zeros add karke), fir left se right digit-by-digit compare karo — digits ki ginti nahi, place value dekho |
| Trailing zero rule | a.b = a.b0 = a.b00 (value same rehti hai) |
| Addition/Subtraction of decimals | Decimal points ko vertically align karo, missing places me 0 bharo, phir normal addition/subtraction karo |
| km ↔ m conversion | 1 km = 1000 m → x m = x/1000 km |
| kg ↔ g conversion | 1 kg = 1000 g → x g = x/1000 kg |
| ₹ ↔ paise conversion | ₹1 = 100 paise → x paise = x/100 rupees |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Students sochte hain ki jitne zyada digits decimal point ke baad honge, number utna hi bada hoga — jaise 3.45 ko 3.5 se bada maan lena, jabki place value dekhne par 3.5 (=3.50) bada hai.
- Trailing zeros add/remove karte waqt confuse ho jaate hain ki value change ho jaati hai — jabki 0.6 aur 0.60 numerically bilkul same hote hain.
- Decimals ko add ya subtract karte waqt decimal points ko align nahi karte, seedhe right-align kar dete hain jaise whole numbers me karte hain — isse galat answer aata hai.
- Missing decimal places me 0 nahi bharte subtraction karte waqt — jaise 9.15 se 8.4 ghatate waqt 8.4 ko 8.40 nahi likhte, jisse borrowing me galti ho jaati hai.
- Unit conversion (km-m, kg-g, rupee-paise) karte waqt decimal point ko galat direction me shift kar dete hain — jaise 250 m ko km me convert karte waqt 0.250 ki jagah 2.50 likh dena.
- Word problems me decimal answer ko unnecessarily round-off kar dete hain ya extra trailing zero laga dete hain bina reason ke, jisse exact measurement value (jaise 0.15 second ka difference) galat represent hoti hai.
Board-Style Important Questions
- School-level periodic tests me decimal comparison aur ordering ke questions frequently poochhe jaate hain — jaise 4-5 decimals ko ascending/descending order me arrange karna
- Real-life measurement word problems (length, weight, money) jisme decimal addition-subtraction karna ho, class tests me common hain
- Place value expansion of a decimal number (jaise 7.243 ko expanded form me likhna) — conceptual questions me repeat hota hai
- Unit conversion problems (km to m, kg to g, rupee to paise) decimal ke saath — worksheets aur unit tests me aate hain
- Trailing zero concept check karne wale True/False ya reasoning-based questions (jaise '0.6 = 0.60 hai ya nahi, reason do') periodic assessments me dekhe gaye hain
Aksar Poochhe Jaane Wale Sawaal
Class 7 Ganita Prakash Chapter 3 'A Peek Beyond the Point' me kya padhaya jaata hai?
Ye chapter decimal numbers ke deep concepts cover karta hai — place value (tenths, hundredths, thousandths), decimal comparison, addition-subtraction of decimals, aur real-life measurement problems (length, weight, capacity, money) jisme decimals use hote hain.
Chapter 1 'Large Numbers Around Us' aur Chapter 3 'A Peek Beyond the Point' me kya connection hai?
Chapter 1 bade whole numbers (lakhs, crores) explore karta hai, jabki Chapter 3 usi number system ko decimal point ke doosri taraf — chhote, precise fractions (tenths, hundredths) tak extend karta hai. Dono milkar number system ki full range samjhate hain — bade se bahut chhote tak.
Decimals compare karne ka sabse aasan tarika kya hai?
Dono decimals ko same number of decimal places tak likho (chote wale me trailing zeros add karke), phir left se right digit-by-digit compare karo. Digits ki ginti dekhna galat tarika hai — hamesha place value dekho.
Kya 0.5 aur 0.50 alag-alag numbers hain?
Nahi, dono same value represent karte hain. Decimal point ke baad right side me trailing zero add karne se number ki value change nahi hoti — 0.5 = 5/10 = 50/100 = 0.50.
Is chapter ko score-friendly banane ke liye kya practice karni chahiye?
Decimal place value expansion, comparison rules, aur addition-subtraction (decimal point align karke) ki daily practice karo. Real-life measurement conversion problems (km-m, kg-g, rupee-paise) bhi bar-bar solve karo kyunki ye exam me application-based questions me common hain.
NCERT Class 7 Maths Ganita Prakash chapter wise solutions kahan milengi is chapter ke exercises ke liye?
Is page pe upar diye gaye in-text aur exercise questions step-by-step, clear working ke saath solve kiye gaye hain — place value, comparison, aur real-life decimal problems sab cover hain taaki concept clarity ke saath practice ho sake.
Class 7 Maths — Saare Chapters
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