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Math Is Easy - Why Does My Telephone Area Code Have To Change!

When our family moved to San Diego in 1973, the area code, 714, was shared with Orange County. Since then San Diego lost 714 and gained 619, 858 and 760. Our phone number has remained the same but our area code has changed from 714 to 619 to 858. Our area code changed because of math!

The phone number is composed of a 3 digit area code, a 3 digit prefix and a 4 digit number. The total phone numbers that can exist is based on the number of area codes, prefixes and 4 digit numbers possible. The 10 digits used for a phone number are 0,1,2,3,4,5,6,7,8,9. How many area codes, prefixes and 4 digit number are possible?

For illustration purposes, suppose that the area code was composed of 2 digits and the digits used are 1 and 2, then there are 4 possible area codes:
11
12
21
22

The number of 2 digit numbers using digits 1 and 2 is calculated as follows:
Digit one can be 1 or 2 for a total of 2 choices.
Digit two can be 1 or 2 for a total of 2 choices.
Digit one choices are mutliplied by digit 2 choices, 2 X 2, for a total of 4 possible 2 digit numbers. Once there are 4 area codes, it is not possible to add anymore area codes unless more digits are allowed and/or the area code is expanded from 2 to 3 digits.


Our current phone number structure allows for a 3 digit area code using digits 0..9.
Digit one can be 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 for a total of 8 choices; 0 is used for calling the operator and 1 is used for dialing a number outside your area code and cannot be the first digit of an area code.
Digit two can be 0 or 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 for a total of 10 choices.
Digit three can be 0 or 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 for a total of 10 choices...
Digit one choices are mutliplied by digit 2 choices and this total is mutliplied by digit 3 choices, 8 X 10 X 10, for a total of 800 possible 3 digit area codes. Some area codes are used for toll free numbers - 800, 866, 877, 888 - and would not be available for geographical area codes, so the total of 800 is reduced by 4 to 796.

Each area code can have a certain number of 3 digit prefixes using digits 0..9.
Digit one can be 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 for a total of 8 choices; 0 is used for calling the operator and 1 is used for dialing a number outside your area code and cannot be the first digit of a prefix..
Digit two can be 0 or 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 for a total of 10 choices.
Digit three can be 0 or 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 for a total of 10 choices...
Digit one choices are mutliplied by digit 2 choices and this total is mutliplied by digit 3 choices, 8 X 10 X 10, for a total of 800 possible 3 digit prefixes. Some prefixes are used for special purposes - 411, 611, 911 - and would not be available for geographical prefixes, so the total of 800 is reduced by 3 to 797.

Each prefix can have a certain number of 4 digit numbers using digits 0..9.
Digit one can be 0 or 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 for a total of 10 choices.
Digit two can be 0 or 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 for a total of 10 choices.
Digit three can be 0 or 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 for a total of 10 choices.
Digit four can be 0 or 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 for a total of 10 choices.
Digit one choices are mutliplied by digit 2 choices, this total is mutliplied by digit 3 choices and this new total is mutliplied by digit 4 choices, 10 X 10 X 10 X 10, for a total of 10,000 possible 4 digit numbers.

In summary, there are 796 possible 3 digit area codes each of which can have 797 possible 3 digit prefixes and each of these can have 10,000 possible 4 digit numbers. Your home phone(s), cell phone(s) and employer phones have created a demand for new phone numbers that will eventually lead to a 4 digit area code or a 4 digit prefix or a 5 digit number and a longer phone number.


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