Question:
How many natural numbers, when converted to base 5 are four- digit numbers ?
How many natural numbers, when converted to base 5 are four- digit numbers ?
Updated On: Aug 21, 2024
- 500
- 470
- 530
- 400
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The Correct Option is A
Solution and Explanation
The smallest and largest four-digit numbers in base 5 are 1000 and 4444, respectively.
Let’s convert the above numbers in base 10 :
(1000)5 = 1 × 53 + 0 × 52 + 0 × 51 + 0 × 50 = 125
(4444)5 = 4 × 53 + 4 × 5² + 4 × 51 + 4 × 50 = 624
Thus, desired number 125 to 624, i.e., 624 - 125 + 1 = 500
So, the correct option is (A) : 500.
Let’s convert the above numbers in base 10 :
(1000)5 = 1 × 53 + 0 × 52 + 0 × 51 + 0 × 50 = 125
(4444)5 = 4 × 53 + 4 × 5² + 4 × 51 + 4 × 50 = 624
Thus, desired number 125 to 624, i.e., 624 - 125 + 1 = 500
So, the correct option is (A) : 500.
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