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Bases (Maths) question?

Number 73 is in base 10

When you write it in base 5 you get

2 * 25 + 4 * 5 + 3 * 1

= 243

Now in the similar way how would you write 23 base 10 in base 12.

How do you compute it.

Update:

Thankyou for all the answers.

One more clarification:-

If A,B,C,D... is to be used after 9 then What will happen if we run out of letters i.e. after ...X,Y,Z

Example:-

75 base 10 in base 38 will be written as _____ (fill in the blanks)

If possible please give me some good links to study.

5 Answers

Relevance
  • None
    Lv 7
    1 decade ago
    Favorite Answer

    This is tricky because you run out of numbers at 9, so you have to substitute letters.

    0,1,2,3,4,5,6,7,8,9,A, B, 10, 11 and so on

    23 consists of one decimal 12 and a decimal 11, so its 1B

  • Anonymous
    1 decade ago

    Like in all bases, you have a one's column. In base 12, the column is the twelve's column.

    ....| 12^3 | 12^2 | 12^1 | 1 |

    ....| 0 | 0 | 1 | 11 |

    From 23 base 10, you can remove one 12, so you put it into the twelve's column. Now you have 11 left over. These go in the one's column.

    Since it is base 12, you can possibly have a 1..11 as a value in any column.

    Sometimes in base twelve, and eleven is written as a 'E'.

    1E or 1 E or | 1 | E | would be the answer. The verticle lines are column delimiters.

  • 1 decade ago

    23 = 12 + 11

    = (1*(12^1))+(11*(12^0))

    = 1B (becaz in 12 base 0 to 9 is same thn 10 = A and 11 = B)

    so, ans = 1B

  • ?
    Lv 7
    1 decade ago

    use 12 as the base for the exponents

    5^1=5

    5^2=25

    5^3=125

    here

    12^1=12

    12^2=144

    6*12^1+1*12^0

    61

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  • 1 decade ago

    imagine that 23 represent months.

    convert that into year(12)+months.=1 year +11months.

    in decimal system first number is 1 and the last is 10.

    in duodecimal system numbers consists of 1,2,3 ....8,9,A,B,10,

    that means 11 decimal is equal to B duodecimal.

    therefore the answer is 1B

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