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Each digit can have one of ten values: any number from 0 through 9. When it reaches 9, just before 10, it starts over at zero again.

Each place value is also worth ten times as much as the last. 10 is worth more than 1, and 10,000 is much more than 100.

If the standard system was, say, base 9, than we would count 0 through 8. When it reached 8, it would start again at zero instead of going on to 9. Each place would be worth 9 times as much as the last.

First few numbers in base 9 (base 10 equivalent in parenthesis): 0 (0), 1 (1), 2 (2), 3 (3), 4 (4), 5 (5), 6 (6), 7 (7), 8 (8), 10 (9), 11 (10), 12 (11), 13 (12), 14 (13), 15 (14), 16 (15), 17 (16), 18 (17), 20 (19)...

The base 2 system, commonly known as the binary system, counts only 0 through 1. Each time it reaches 1, it goes back to zero again, then counts to 1 again. Each place is worth twice as much as the last.

First few numbers in base 2 (base 10 equivalent in parenthesis): 0 (0), 1 (1), 10 (2), 11 (3), 100 (4), 101 (5), 110 (6), 111 (7), 1000 (8), 1001 (9), 1010 (10), 1011 (11), 1100 (12), 1101 (13), 1110 (14), 1111 (15), 100000 (16)...

Another common system is base 16, known as hexadecimal. It counts through 0 to 9, then keeps counting A (10), B (11), C (12), D (13), E (14), and F (15), and then resets to zero. The total number of possible values for each digit is 16. And, of course, each place value is worth 16 times the last.

First few numbers in base 16 (base 10 equivalent in parenthesis): 0 (0), 1 (1), 2 (2), 3 (3), 4 (4), 5 (5), 6 (6), 7 (7), 8 (8), 9 (9), A (10), B (11), C (12), D (13), E (14), F (15), 10 (16), 11 (17), 12 (18), 13 (19), 14 (20), 15 (21), 16 (22), 17 (23), 18 (24), 19 (25), 1A (26), 1B (27)...

Besides these basic changes, you count similarly to if you were counting base 10.

Q: Why is the standard number system called a base 10 system?

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Continue Learning about Other Math

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It is the number 16.

The number system that uses a base of 10 and the valid numbers are 0 to 9 is the decimal system.

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