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denominator-selection MCQ Questions for Class 10

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6 questions tagged with denominator-selection.

Question 1/6 Expert Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 21

किस सरलतम हर से ठीक (8) दशमलव स्थान मिलेंगे?

Which reduced denominator will give exactly (8) decimal places?

Explanation opens after your attempt
Correct Answer

B. \(2^8\cdot 5^3\)

Step 1

Concept

For exactly (8) places, the larger exponent of (2) and (5) must be (8). Only \(2^8\cdot 5^3\) satisfies this.

Step 2

Why this answer is correct

The correct answer is B. \(2^8\cdot 5^3\). For exactly (8) places, the larger exponent of (2) and (5) must be (8). Only \(2^8\cdot 5^3\) satisfies this.

Step 3

Exam Tip

ठीक (8) स्थानों के लिए (2) और (5) की बड़ी घात (8) होनी चाहिए। दिए विकल्पों में केवल \(2^8\cdot 5^3\) यह शर्त पूरी करता है।

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Question 2/6 Expert Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 20

किस सरलतम हर से ठीक (7) दशमलव स्थान मिलेंगे?

Which reduced denominator will give exactly (7) decimal places?

Explanation opens after your attempt
Correct Answer

B. \(2^7\cdot 5^3\)

Step 1

Concept

For exactly (7) places, the larger exponent of (2) and (5) must be (7). Only \(2^7\cdot 5^3\) satisfies this.

Step 2

Why this answer is correct

The correct answer is B. \(2^7\cdot 5^3\). For exactly (7) places, the larger exponent of (2) and (5) must be (7). Only \(2^7\cdot 5^3\) satisfies this.

Step 3

Exam Tip

ठीक (7) स्थानों के लिए (2) और (5) की बड़ी घात (7) होनी चाहिए। दिए विकल्पों में केवल \(2^7\cdot 5^3\) यह शर्त पूरी करता है।

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Question 3/6 Expert Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 19

कौन-सा हर सरलतम भिन्न में ठीक (6) दशमलव स्थान देगा?

Which denominator in a reduced fraction will give exactly (6) decimal places?

Explanation opens after your attempt
Correct Answer

B. \(2^6\cdot 5^2\)

Step 1

Concept

For exactly (6) places, the larger exponent of (2) and (5) must be (6). Only \(2^6\cdot 5^2\) has larger exponent (6).

Step 2

Why this answer is correct

The correct answer is B. \(2^6\cdot 5^2\). For exactly (6) places, the larger exponent of (2) and (5) must be (6). Only \(2^6\cdot 5^2\) has larger exponent (6).

Step 3

Exam Tip

ठीक (6) स्थानों के लिए (2) और (5) की बड़ी घात (6) होनी चाहिए। केवल \(2^6\cdot 5^2\) में बड़ी घात (6) है।

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Question 4/6 Hard Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 21

कौन-सा हर सरलतम भिन्न में असांत आवर्ती दशमलव देगा?

Which denominator in a reduced fraction will give a non-terminating recurring decimal?

Explanation opens after your attempt
Correct Answer

D. \(2^4\cdot 5\cdot 23\)

Step 1

Concept

For a non-terminating recurring decimal, the reduced denominator must have a prime factor other than (2) and (5).

Step 2

Why this answer is correct

\(2^4\cdot 5\cdot 23\) contains (23). Hence it gives a non-terminating recurring decimal.

Step 3

Exam Tip

Even one extra prime factor prevents termination. चरण 1: असांत आवर्ती दशमलव के लिए सरलतम हर में (2) और (5) के अलावा कोई अभाज्य गुणनखंड होना चाहिए। चरण 2: \(2^4\cdot 5\cdot 23\) में (23) मौजूद है। इसलिए यह असांत आवर्ती दशमलव देगा। चरण 3: केवल एक अतिरिक्त अभाज्य गुणनखंड भी सांतता रोक देता है।

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Question 5/6 Hard Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 20

कौन-सा हर (q) ऐसी सरलतम भिन्न \(\frac{p}{q}\) दे सकता है जिसका दशमलव ठीक (5) स्थानों पर समाप्त हो?

Which denominator (q) can give a reduced fraction \(\frac{p}{q}\) whose decimal terminates exactly after (5) places?

Explanation opens after your attempt
Correct Answer

B. (3125)

Step 1

Concept

For exactly (5) decimal places, the larger exponent of (2) and (5) in the reduced denominator must be (5).

Step 2

Why this answer is correct

\(3125=5^5\), so it gives (5) places. (250) and (40) give fewer places, while \(1600=2^6\cdot 5^2\) gives (6) places.

Step 3

Exam Tip

Compare the prime exponents of the denominator. चरण 1: ठीक (5) दशमलव स्थानों के लिए सरलतम हर में (2) और (5) की बड़ी घात (5) होनी चाहिए। चरण 2: \(3125=5^5\), इसलिए यह (5) स्थान देता है। (250) और (40) कम स्थान देते हैं, जबकि \(1600=2^6\cdot 5^2\) (6) स्थान देगा। चरण 3: हर के अभाज्य घातों की तुलना करें।

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Question 6/6 Hard Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 19

यदि \(\frac{7}{q}\) का दशमलव प्रसार सांत है और \(\frac{7}{q}\) सरलतम रूप में है, तो (q) के लिए कौन-सा विकल्प संभव है?

If \(\frac{7}{q}\) has a terminating decimal expansion and is in lowest form, which option is possible for (q)?

Explanation opens after your attempt
Correct Answer

B. (80)

Step 1

Concept

A reduced denominator must contain only (2) and (5).

Step 2

Why this answer is correct

\(80=2^4\cdot 5\), so it is possible. (48), (84), and (98) contain primes like (3) or (7).

Step 3

Exam Tip

If lowest form is given, check the prime factors of the denominator directly. चरण 1: सरलतम हर में केवल (2) और (5) होने चाहिए। चरण 2: \(80=2^4\cdot 5\), इसलिए यह संभव है। (48), (84), और (98) में (3) या (7) जैसे गुणनखंड हैं। चरण 3: सरलतम रूप बताया हो तो हर की सीधी अभाज्य जाँच करें।

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