hedipaldi said:Homework Statement
How to compute the base 3 decimal expansion of 1/4?
Homework Equations
The Attempt at a Solution
I tried sums of geometric sequences,but i need a clue for the computation.
hedipaldi said:So far i already got.How to proceed?
The base 3 decimal expansion is a representation of a number in the base 3 number system. It consists of digits 0, 1, and 2 and follows the same principles as the base 10 decimal system but with a different base.
The base 3 decimal expansion is calculated by dividing a number by 3 and noting the remainder. The remainder becomes the least significant digit, and the quotient is divided again until the quotient becomes 0. The digits are then arranged in reverse order to get the base 3 decimal expansion of the number.
Using different bases in the decimal expansion allows us to represent numbers in a more concise and efficient way. In base 3, there are only 3 digits, making it easier to perform calculations and store large numbers.
The base 3 decimal expansion is similar to other bases in terms of principles, but it uses a different set of digits. For example, in the binary system (base 2), there are only 2 digits (0 and 1), while in the hexadecimal system (base 16), there are 16 digits (0-9 and A-F).
Yes, all numbers can be represented in the base 3 decimal expansion. However, some numbers may have recurring digits and may not have a finite representation in base 3, just like how 1/3 has a recurring decimal in the base 10 system.