| --- |
| source: ncert_exercises |
| topic: numbers |
| class_level: class_10 |
| chapter: ch1 |
| exercise: ex1.3 |
| difficulty: beginner |
| --- |
| |
| Class 10 | Ch1: Real Numbers | Exercise 1.3 |
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| Decimal Expansions: p/q terminates iff q = 2įµĆ5āæ (after simplification). |
| If q has other prime factors ā non-terminating repeating. |
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| Q1. Without performing division, state whether decimal expansions terminate or not: |
| (i) 13/3125 (ii) 17/8 (iii) 64/455 (iv) 15/1600 (v) 29/343 |
| (vi) 23/(2Ā³Ć5Ā²) (vii) 129/(2Ā²Ć5ā·Ć7āµ) (viii) 6/15 (ix) 35/50 (x) 77/210 |
| Answer: |
| (i) 3125=5āµ. Terminates. ā
|
| (ii) 8=2Ā³. Terminates. ā
|
| (iii) 455=5Ć7Ć13. Has 7,13 ā Non-terminating. ā
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| (iv) 1600=2ā¶Ć5Ā². Terminates. ā
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| (v) 343=7Ā³. Non-terminating. ā
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| (vi) q=2Ā³Ć5Ā². Terminates. ā
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| (vii) Has 7āµ ā Non-terminating. ā
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| (viii) 6/15=2/5. q=5. Terminates. ā
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| (ix) 35/50=7/10=7/(2Ć5). Terminates. ā
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| (x) 77/210=11/30=11/(2Ć3Ć5). Has 3 ā Non-terminating. ā
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| Q2. Write decimal expansions of the terminating ones above: |
| (i) 13/3125=13/5āµ=13Ć2āµ/10āµ=416/100000=0.00416. ā
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| (ii) 17/8=17Ć125/1000=2125/1000=2.125. ā
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| (iv) 15/1600=15/(2ā¶Ć5Ā²)=15Ć5ā“/2ā¶Ć5ā¶=15Ć625/10ā¶=9375/10ā¶=0.009375. ā
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| (vi) 23/(2Ā³Ć5Ā²)=23Ć5/(2Ā³Ć5Ā³)=115/1000=0.115. ā
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| (viii) 2/5=4/10=0.4. ā
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| (ix) 7/10=0.7. ā
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