# Base 6 to Base 10: 121.025255045 and 25.503452

#### Amymath

##### New member
I need help in converting two numbers that are in base 6 to base 10. I can do the whole numbers without a problem but after the decimal point I can't solve it.

121.025255045
25.503452

Amymath

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#### ksdhart2

##### Senior Member
When converting from one base to another, I find it helpful to break the number apart into fractions, so as to better understand what's going on "under the hood." In this case, your two numbers are:

1 * 62 + 2 * 61 + 1 * 60 + 0/6 + 2/62 + 5/63 + 2/64 + 5/65 + 5/66 + 0/67 + 4/68 + 5/69

Your goal in this exercise is to convert it to base 10, or the following form:

? * 102 + ? * 101 + ? * 100 + ?/10 + ?/102 + ... + ?/109

See if doing this helps you tackle the problems.

#### stapel

##### Super Moderator
Staff member
I need help in converting two numbers that are in base 6 to base 10. I can do the whole numbers without a problem but after the decimal point I can't solve it.

121.025255045
25.503452
What methods, rules, formulas, algorithms, or other info did they give you in class for this? How far have you gotten in applying that information? Where are you getting stuck?

#### Ishuda

##### Elite Member
I need help in converting two numbers that are in base 6 to base 10. I can do the whole numbers without a problem but after the decimal point I can't solve it.

121.025255045
25.503452

Amymath
About the same kind of approach as ksdhart2. If you use 'scientific notation', a 'decimal' number can this can be written as a whole number plus the base to an exponent.

As a simple example 25.3 base six can be written as 253 * 6-1. Now convert 253 to base 10 [=105] and divide by 6 [=17.5].

#### Amymath

##### New member
About the same kind of approach as ksdhart2. If you use 'scientific notation', a 'decimal' number can this can be written as a whole number plus the base to an exponent.

As a simple example 25.3 base six can be written as 253 * 6-1. Now convert 253 to base 10 [=105] and divide by 6 [=17.5].
I'm still struggling to solve. I wish I had my fancy high school calculator.
This is from a Geocaching puzzle. I need the numbers to work out the coordinates.

The puzzle (in short):
According to the aliens records they will start their attack from the coordinates:
s 53 121.025255045
e 411 25.503452

We know the aliens only have 3 fingers on each hand (hence why I thought it was in base 6).
I know I'm on the right track as the first numbers convert perfectly (as all coordinates in Australia start with s33 and e151). I just can't get the decimal point numbers as I haven't had to do math for a looooong time.

#### Amymath

##### New member
Okay. I think I got it thanks to all your help.
121.025255045 converts to 17.8509945. (I'm not sure if I did this one right)
and
25.503452 converts to 49.081

is it right?

#### missinglynk3

##### New member
Hi Amymath, did you get a final answer for this?

#### Harry_the_cat

##### Senior Member
Okay. I think I got it thanks to all your help.
121.025255045 converts to 17.8509945. (I'm not sure if I did this one right)
and
25.503452 converts to 49.081

is it right?
Your numbers are correct but you have them mixed up:
121.025255045 converts to 49.081
25.503452 converts to 17.8509945
Somewhere at North Head, Sydney by the looks of things!!