does anyone know how to convert a number from base 6 to 10?

Question

for example, how to convert (4516) in base 6 to base 10?


thanks

Answer 1

4516 cant be a base six number to begin with! You count from 0 to 5 and then it would carry, henceforth and towidth, there cant be the digit 6 in the number! Only 0 thru 5!

Answer 2

To convert a number from base 6 to base ten write the number down on a sheet of paper

4 5 1 6 Now think of it this way:

The 6 represents single digits
The 1 represents units of six
The 5 represents units of thirty-six
The 4 represents units of two hundred sixteen

Then you must convert and add:
6 + 6 + 180 + 864 = 1056
This means that 4516 base6 = 1056 base10

Answer 3

In any base (including 10), the rightmost position is 1s; the next position moving to the left is b^1, then b^2, b^3 and so forth, where b is the base. (In base 10, that works out to 1s, 10s, 100s, etc.)

4516 in base 6 is 4*6^3 + 5*6^2 + 1*6^1 + 6*6^0
= 864 + 180 + 6 + 6 = 1056 in base 10.

Answer 4

Well, in base 6 the number 4516 doesn't exist, as the digit "6" isn't allowed.

1. To convert, start with zero.

2. Add the first digit.

3. If the digit you added is the last digit, stop.

4. Otherwise, multiply by six and add the next digit; go to step 3.

So, to convert 4513 to base 10...

0+4=4
4*6+5=29
29*6+1=175
175*6+3=1053

Ergo, 4513(6) = 1053(10).

Answer 5

An example might help.

Example
Convert the base 6 number 214 to a base ten number
214 base 6 may be shown as ;-
6²--------6-------1
2---------1-------4 which becomes:-

(2 x 36) + (1 x 6) + (4 x 1) = 72 + 6 + 4 = 82 in base ten which leads to your question:-

6³-------6²-------6-------1
4--------5--------1-------6

4 x 6³ + 5 x 6² + 1 x 6 + 6 x 1 = 864 + 180 + 6 + 6 =1056 in base ten

Answer 6

ok, you want to start from right to left. The first digit is 6^0 or 1, second is 6^1 or 6, the next 6^2 or 36 and 4th is 6^3 or 216.


So first number 6 is just 6(1).
Second is 1(6) = 6
third is 5(36) = 180
fourth 4(216)=864

Add them all up 6 + 6 + 180 + 864=1056

Answer 7

To convert 4516 in base 6 to base 10, as stated, the definition would be

4*6^3 + 5*6^2 + 1*6^1 + 6*6^0

Instead of calculating this, we can use what is known as "Horner's Algorithm" to reduce the size of the multiplications you do.
Going from left to right, for 4516:

1) 4 x 6 = 24.
2) 24 + 5 = 29
3) (29 x 6) + 1 = 175
4) (175 x 6) + 6 = 1056

See http://www.hitxp.com/math/arth/210804.htm for more details.

Answer 8

nicely, you remember the which technique of the radix element in different bases - it in basic terms signifies that digits after the point are taken to adverse powers of the bottom. So, in base 6, 0.44444... potential 4*6^(-a million) + 4*6^(-2) + 4*6^(-3) + 4*6^(-4)... etc. to discover the decimal equivalent for an arbitrary irrational volume, there is not something left to do yet sum the limitless sequence. hence, nonetheless, the volume is rational, which signifies that by technique of grouping collectively the repeating sequence, to procure a geometrical sequence that could be summed actual (that's the case commonly for rational numbers). subsequently, hence, we've: [ok=a million, ?]?4/6^ok that is an same as: 4/6 * [ok=0, ?]?a million/6^ok by technique of the formula for summing a geometrical sequence, that's: 4/6 * a million/(a million-a million/6) 4/6 * a million/(5/6) 4/6 * 6/5 4/5 Which has the obtrusive decimal representation of 0.8 .