How many times is the digit 5 written when listing all numbers from 1 to 100000?
Answers
Answer:
Step-by-step explanation:
Given:
Between the numbers 0 to 10, number 5 appears 1 time.
Between the numbers 0 to 99, 5 appears 20 times I.e. (5, 15, 25, 35, 45, 50, 51, 52, 53, 54, 55, 56, 57,58, 59, 65, 75, 85, 95)
Note: In the number 55, 5 appears 2 times.
Therefore, 5 appears 20 times between 0 and 99.
In the same way,
From 0-99, 5 appears 20 times
From 100-199, 5 appears 20 times
From 200-299, 5 appears 20 times
From 300-399, 5 appears 20 times
From 400-499, 5 appears 20 times
From 600-699, 5 appears 20 times
From 700-799, 5 appears 20 times
From 800-899, 5 appears 20 times
From 900-999, 5 appears 20 times
From 500-509 i.e. (500, 501, 502, 503, 504, 505, 506, 507, 508, 509 ) 5 appears 11 times
From 510-519 I.e. (510, 511, 512, 513, 514, 515, 516, 517, 518, 519) 5 appears 11 times
From 520-529 I.e. (520, 521, 522, 523, 524, 525, 526, 527, 528, 529) 5 appears 11 times
From 530-539 I.e. (530, 531, 532, 533, 534, 535, 535, 537, 538, 539) 5 appears 11 times
From 540-549 I.e. (540, 541, 542, 543, 544, 545, 546, 547, 548, 549) 5 appears 11 times
From 550-559 I.e. (550, 551, 552, 553, 554, 555, 556, 557, 558, 559) 5 appears 21 times
Similarly from 560-569, 570-579, 580-589, 590-599 5 will appear 11 times in each case I.e. 44 times between 560–599
From 0-1000, 5 appears 300 times.
Similarly, From 1000–1999, 2000–2999, 3000–3999, 4000–4999, 6000–6999, 7000–7999, 8000–8999, 9000–9999, 5 appears 300 times in each of the cases
From 5100–5199, 5 as it is appears 100 times before and after every number i.e. (5100, 5101, 5102..5199) and according to our earlier derivation between 100–199, 5 appears 20 times.
Therefore it appears 120 times between 5100–5199.
Similarly, From 5200–5299, 5300–5399, 5400–5499, 5600–5699, 5700–5799, 5800–5899, 5900–5999: 5 appears 120×9 = 1080 times.
From 5500–5599, 5 appears 100 times before and after every number and according to our earlier derivation between 500–599, 5 appears 120 times.
Therefore, 5 appears 100+120= 220 times between 5500–5599
Thus, Between 5000–5999, 5 appears 120×9+220= 1080+220= 1300 times.
Thus 5 appears 4000 times between 1 to 100000.
Answer:
answer is 4000 because in 10 one 5 is come so in 1000=4000 5 is come