- #1

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My question is, how can i figure out fractions to decimals with different bases?

basically, i would like to know how to use different bases other than 10.

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- Thread starter lvlastermind
- Start date

- #1

- 101

- 0

My question is, how can i figure out fractions to decimals with different bases?

basically, i would like to know how to use different bases other than 10.

- #2

chroot

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Consider the following division problem in binary, which has only digits: 0 and 1.

100000 / 1000

Set up your long division as usual:

Code:

```
______1__
1000 | 100000
- 1000
---------
000000
```

Of course, this makes sense: 1000 in binary is 8 in decimal. 100000 in binary is 32 in decimal. 32 / 8 = 4, or 100 in binary.

All of the normal division, multiplication, addition, and subtraction algorithms you learned in grade school work exactly the same way in any base.

If you have a specific question you're trying to solve, please let me know, and I'll help you.

- Warren

- #3

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- #4

Integral

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Using base 10 arithmetic, multiply your decimal number by the new base. The integer part is a digit in the new base. Repeat the process with the fractional part. Each repetition generates the next digit.

For example .1 in base 10 to base 2

2*.1 = 0.2

integer part =0 so your first digit is 0

.1_{10}~ .0_{2}

Now take the fractional part and repeat.

2 *.2 = 0.4

.1_{10}~ .00_{2}

repeat

2*.4 =0.8

.1_{10}~ .000_{2}

repeat

2*.8 = 1.6

Finally! a non zero digit!

.1_{10}~ .0001_{2}

2*.6= 1.2

.1_{10}~ .00011_{2}

2*.2=0.4

.1_{10}~ .000110_{2}

now you can observe that a pattern is emerging.

This same method can be used for conversion to any base.

For example .1 in base 10 to base 2

2*.1 = 0.2

integer part =0 so your first digit is 0

.1

Now take the fractional part and repeat.

2 *.2 = 0.4

.1

repeat

2*.4 =0.8

.1

repeat

2*.8 = 1.6

Finally! a non zero digit!

.1

2*.6= 1.2

.1

2*.2=0.4

.1

now you can observe that a pattern is emerging.

This same method can be used for conversion to any base.

Last edited:

- #5

- 101

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thanks alot

- #6

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so would .1 (base 10) equal .021262 and so fourth in base 5?

- #7

jcsd

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lvlastermind said:so would .1 (base 10) equal .021262 and so fourth in base 5?

No, 0.1 in base 5 would equal [itex]0.\dot{2}[/itex]. Remember base 5 would only use the digits 0, 1, 2, 3 and 4 so that 6 can't be in there.

- #8

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hmm....

can you show me you work for that?

For some reason im having trouble..

can you show me you work for that?

For some reason im having trouble..

- #9

jcsd

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(1/10)/(1/5) = 0 R 1/10

(1/10)/(1/25) = 2 R 1/50

(1/50)/(1/125) = 2 R 1/250

(1/250)/(1/625) = 2 R 1/1250

(1/1250)/(1/3125) = 2 R 1/6250

That gives us so far 0.02222

Now we've probably already guessed that this is going to be a a recurring number, infact we should of seen this about the begining as 1/10 = (1/5)(1/2) and x in the equation [itex] \frac{x}{5^n} = \frac{1}{2}[/itex] can never be an integer.

- #10

- 101

- 0

alright, thx

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