Class X Math all chapters Question Solved NCERT

Exercise 1.3 Class X Math

Decimal Expansion of Rational Numbers
(সমাপ্ত আৰু অসীম দশমিক বিস্তাৰ)

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🟢 Q1. Write the decimal expansion of the following rational numbers and state whether they are terminating or non-terminating repeating.

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(i) 13/3125

Solution (English):
3125 = $5^5$55
Denominator has only prime factor 5.$$\frac{13}{3125} = 0.00416$$312513​=0.00416

👉 Terminating decimal

অসমীয়া:
হৰত কেৱল 5 আছে।
অতএব দশমিক সমাপ্ত।
উত্তৰ = 0.00416

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(ii) 17/8

Solution:
8 = $2^3$23$$\frac{17}{8} = 2.125$$817​=2.125

👉 Terminating decimal

অসমীয়া:
2 ৰ ঘাত মাত্ৰ আছে।
উত্তৰ = 2.125 (সমাপ্ত)

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(iii) 64/455

Solution:
455 = 5 × 7 × 13
Denominator contains prime factors other than 2 and 5.

👉 Non-terminating recurring decimal

অসমীয়া:
5 ৰ বাহিৰেও 7, 13 আছে।
👉 অসমাপ্ত পুনৰাবৃত্ত দশমিক

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(iv) 15/1600

Solution:
1600 = $2^6 × 5^2$26×52$$\frac{15}{1600} = 0.009375$$160015​=0.009375

👉 Terminating decimal

অসমীয়া:
হৰফ = $2^m × 5^n$2m×5n
অতএব সমাপ্ত দশমিক = 0.009375

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(v) 29/343

Solution:
343 = $7^3$73
Prime factor ≠ 2 or 5.

👉 Non-terminating recurring decimal

অসমীয়া:
7 আছে → সমাপ্ত নহয়
👉 অসমাপ্ত পুনৰাবৃত্ত

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🟢 Q2. Find the decimal expansion of 7/125.

Solution:
125 = $5^3$53$$\frac{7}{125} = 0.056$$1257​=0.056

👉 Terminating decimal

অসমীয়া:
উত্তৰ = 0.056 (সমাপ্ত)

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🟢 Q3. Express 23/50 in decimal form.

Solution:$$\frac{23}{50} = \frac{46}{100} = 0.46$$5023​=10046​=0.46

👉 Terminating

অসমীয়া:
50 = $2 × 5^2$2×52
উত্তৰ = 0.46

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🟢 Q4. Without actually performing the division, state whether the following have terminating decimal expansion:

(i) 13/40

40 = $2^3 × 5$23×5
👉 Terminating

অসমীয়া: সমাপ্ত

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(ii) 7/6

6 = $2 × 3$2×3
👉 Contains 3 → Non-terminating

অসমীয়া: অসমাপ্ত

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(iii) 15/125

125 = $5^3$53
👉 Terminating

অসমীয়া: সমাপ্ত

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🟢 Q5. Write the decimal expansion of 5/8.

Solution:$$\frac{5}{8} = 0.625$$85​=0.625

👉 Terminating

অসমীয়া:
উত্তৰ = 0.625

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📌 Important Rule (VERY IMPORTANT FOR EXAM)

✅ Terminating Decimal:

If denominator (in lowest form) =$$2^m × 5^n$$2m×5n

❌ Non-terminating Recurring:

If denominator has any prime factor other than 2 or 5

অসমীয়া সংক্ষেপে:
✔ 2 আৰু 5 মাত্ৰ → সমাপ্ত
❌ অন্য মৌলিক সংখ্যা → অসমাপ্ত

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