What would be the base 8 representation of decimal number 64?

Question

What would be the base 8 representation of decimal number 64?

Can someone tell me 2 methods?( long way, and quick short-cut method)

Answer 1

OK let's see if we can get it for you:

Base powers work like this

10 to the 0 power = 1
10 to the 1 power =10
10 to the 2 power =100
10 to the 3 power =1000.
10 to the 4 power =10000 etc., etc.

So when we say you have a number 4,256 that is like saying I have the following

4 x 10^3 = 4000; 2 x 10^2 = 200; 5 x 10^1 = 50; 6 x 10^0 = 6

Add them up you get 4,256. Note the notation ^ means to the power of.

OK - now lets try the base power of 8.

8^0 = 1
8^1= 8
8^2= 64
8^3= 512
8^4= 4096

OK
Picture this for your number
------------------------------...
8^3 / 8^2 / 8^1 / 8^0
------------------------------...
So you need 1 8^2s, 0 8^1s and 0 8^0s so

100 base 8 = 64 base 10


Now another way is to use base2.
1000 base 2 = 1 base8
so 1000000 base 2 = 100 base8
So if 64 is 1000000 base 2., it is also 100 base 8 or

1* 2^6 = 1*8^2 = 64

Hope this helps.

Answer 2

It would be 100.

The way you do this is by figuring out what each place is worth in base 8.

Example:

In base 10 the number 123 is = 1 * 10^2 + 2 *10^1 + 3 * 10^0

But, in base 8 the number 123 is = 1 * 8^2 + 2 * 8^1 + 3 * 8^0
Which is = 64 + 16 + 3 = 83 in base 10

So, since you want 64 in base 10 converted to base 8 it's quick and easy to see it's 100.

The long way to do this is to find the value in of the placeholders in a base 8 number i.e. 1, 8, 64, 512......., and if the base 10 number you want is in between two of them that's where to start.

So, if the number is 300 in base 10, you know 64 goes into it 4 times (4 * 64 = 256) leaving 44. 8 goes into 44 5 times leaving 4. So the result is 454. Checking we see:

4 * 8^2 + 5 * 8^1 + 4 * 8^0
4(64) + 5(8) + 4(1)
256 + 40 + 4
300

Hope that helps.

Answer 3

oooooooooooh this my favorite kind of math problem

decimal number means it is base10

64 in base 10
yes
ok
the bases in base 8

are
8^0 and 8^1 and 8^2 and 8^3 and so on
note ^x means a power

so 8 * 8 * 8 for 8^3 = 512 does 512 go into 64
no
so on to the lower power 8^2
does 8 * 8 = 64 yes
fully so 8^2 goes in to 64 1 time so

there is no need for any ones
1 0 0
8^2 8^1 8^0
| | |
64 8 1
because any # to zero power equals one the first part will always equal one
and to prounonce the answer 100
say one zero zero because um i cant explain just do it

to un solve something in base 8

to find out what 100 is which we already know is 64

just multiply it all out like 1* 8^2 +0*8^1+0*8^0 whcih equals 64

now look at my second answer for the short way

im 12!!!

Answer 4

Start by writing the powers of 8 in reverse order. Start with 1 then 8, then by 64, etc. You can stop when the next number would be bigger than your number.
64-8-1

Now work left to right. How many 64's in your number... 1 right?
So put a 1 under the 64.

64-8-1
1

Now subtract one 64 from your number (this is easy in this case) and you have zero. Now you are done. Just put zeros in the remaining spots
64-8-1
1-0-0

So the answer is 64 is written as 100 base 8

Answer 5

Isn't 64 in base 8 represented as 100?

100 base 8 = 1 * 8^2 + 0 * 8^ 1 + 0 * 8^0

The same would be true in base 10

64 base 10 = 6 * 10^1 + 4 * 10^0

Answer 6

64 converted to base 8 is 10 since 1*8^2+0*8=64...