Page 20 - NUMINO Challenge_C2
P. 20
Basic Concepts Number of 7’s
In the numbers from 1 to 99, every digit except 0 appears 20 times.
For example, in the numbers from 1 to 99, the digit 7 appears:
7: 7, 17, 27, 37, 47, 57, 67, 77, 87, 97 10 times
7 : 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 10 times
Therefore, 7 appears a total of 20 times.
In the numbers from 1 to 999, every digit except 0 appears 300 times.
For example, in the numbers from 1 to 999, the digit 7 appears:
7: 7, 17, 27, , 977, 987, 997 100 times
7 : 70, 71, 72, , 977, 978, 979 100 times
7 : 700, 701, 702, , 797, 798, 799 100 times
Therefore, 7 appears a total of 300 times.
Example How many times does the digit 2 appear in the numbers from 1 to
300?
Class Notes
In the numbers from 1 to 300, the digit 2 can appear in the ones place, the tens
place, or the hundreds place.
Numbers with 2 in the ones place ( 2): 002, 012, 022, 032, , 282, 292
Numbers with 2 in the tens place ( 2 ): 020, 021, 022, 023, , 228, 229
Numbers with 2 in the hundreds place (2 ): 200, 201, 202, 203, , 298, 299
The digit 2 appears in the ones place 29 0 1 times, from numbers
2 to 2.
The digit 2 appears in the tens place 29 0 1 times, which is the same as
the number of numbers that lie between 0 and 29.
The digit 2 appears in the hundreds place 99 0 1 times, which is the
same as the number of numbers that lie between 0 and 99.
Therefore, in the numbers from 1 to 300, the digit 2 appears a total of
times.
17Number and Operations
In the numbers from 1 to 99, every digit except 0 appears 20 times.
For example, in the numbers from 1 to 99, the digit 7 appears:
7: 7, 17, 27, 37, 47, 57, 67, 77, 87, 97 10 times
7 : 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 10 times
Therefore, 7 appears a total of 20 times.
In the numbers from 1 to 999, every digit except 0 appears 300 times.
For example, in the numbers from 1 to 999, the digit 7 appears:
7: 7, 17, 27, , 977, 987, 997 100 times
7 : 70, 71, 72, , 977, 978, 979 100 times
7 : 700, 701, 702, , 797, 798, 799 100 times
Therefore, 7 appears a total of 300 times.
Example How many times does the digit 2 appear in the numbers from 1 to
300?
Class Notes
In the numbers from 1 to 300, the digit 2 can appear in the ones place, the tens
place, or the hundreds place.
Numbers with 2 in the ones place ( 2): 002, 012, 022, 032, , 282, 292
Numbers with 2 in the tens place ( 2 ): 020, 021, 022, 023, , 228, 229
Numbers with 2 in the hundreds place (2 ): 200, 201, 202, 203, , 298, 299
The digit 2 appears in the ones place 29 0 1 times, from numbers
2 to 2.
The digit 2 appears in the tens place 29 0 1 times, which is the same as
the number of numbers that lie between 0 and 29.
The digit 2 appears in the hundreds place 99 0 1 times, which is the
same as the number of numbers that lie between 0 and 99.
Therefore, in the numbers from 1 to 300, the digit 2 appears a total of
times.
17Number and Operations
