1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
maxonik [38]
3 years ago
13

How to convert a whole base 10 number to another base?

Mathematics
1 answer:
KatRina [158]3 years ago
6 0
In base 10, the positional of each digit represents which power of 10 that position is taken to and the number represents how many of them you have, i.e. the number 532

100s, 10s, 1s
5.........3......2

Any other base works the same way but instead of powers of 10, we use whatever power that base is, so the number 25 in base 2:

16s, 8s, 4s, 2s, 1s
1.......1......0....0....1

To convert from base 10 to a different base, first find the highest power (position) in that base that is less than your numbers, you can do that by taking the log and round down (for the power) and take ithe base to that number (for the value). E.g. for the number 83, in base 2 you would do log2(83)=6 (rounded down), so that has the 2^6=64s place. Again with base 53, log3(83)=4, and is the 3^4= 81s place. (You can do log(83)/log(2)=6 if you can't change the base on your calculator).

So, starting with the highest you have just found, list all the powers of the base (just divide by the base each time), so base 2:

64s, 32s, 16s, 8s, 4s, 2s, 1s

Next you just go from highest to lowest, and, starting with your number, see how many of each position you can fit into it (keeping the number inside your base), subtracting the amount from it each time you do so. E.g. for base 2, number 83:

64s, 32s, 16s, 8s, 4s, 2s, 1s
1.........0.......1......0....0....1......1
83.....19......3.....3....3....1.....0

So 83 in base 2 is 1010011.

In base 3, for the number 140:
81s, 27s, 9s, 3s, 1s
1........2......0....1.....2
140..59......5...2....0

Starting at 140, 1 81 will fit into it so place a 1 in the 81s place and subtract 1*81 from 140 to get 59. 2 27s fit into 59 so write 2 under the 27s place and subtract 2*27=54 from 59 = 5. Continue and you should always end up with 0 remaining.

So 140 in base 3 is 12012.

I hope you understand this, it looks abit complicated at first but it's quite easy when you get the hang of it.
You might be interested in
Someone please answer.
lutik1710 [3]

Answer:

I don't no sorry for that

3 0
3 years ago
Toms son works in a sports store.Toms son earns a commision. He makes 2.5% of the amount he sells. Last week he sold $900 worth
siniylev [52]

Answer:

22.5

Step-by-step explanation:

2.5/100= 0.0250

0.025 x 900 = 22.5

5 0
3 years ago
-2 (3.1) find the product
marin [14]

Answer:

-6.2

Step-by-step explanation:

just because.

5 0
3 years ago
Sasha is collecting cans to recycle.When she collected 180 cans she knew she haad reached 60% of her goal How many more cabs doe
Arturiano [62]
It would be 60 because 180 minus 60 is 60
8 0
3 years ago
PLEASE HELP!!!!! 3, 8, 13, 18, 23, ....<br><br> The recursive formula for this sequence is:
rodikova [14]

Answer:

a₈ = 37

Step-by-step explanation:

The given arithmetic sequence is: 3, 8, 13, 18, 23, . . .

The recursive formula for the sequence is: $ a_n = a_{n - 1} + 5 $

Here, $ a_n $ represents the $ n^{th} $ of the sequence.

And, $ a_{n - 1} $ represents the $ (n - 1)^{th} $ of the sequence.

'+5' denotes that '5' is added to the $ (n - 1)^{th} $ term to get the $ n^{th} $ term. In other words, the difference between two consecutive numbers in the sequence is 5.

Now, we are asked to find a₈ i.e., n =8.

Substituting in the recursive formula we get: a₈ = a₍₈₋ ₁₎ + 5 = a₇ + 5.

So, to determine a₈ we need to know a₇. From the sequence we see that a₅ = 23.

⇒ a₆ = 23 + 5 = 28.

⇒ a₇ = 28 + 5 = 32.

⇒ a₈ = 32 + 5 = 37.

Therefore, the $ 8^{th} $ term of the sequence is 37.

8 0
3 years ago
Other questions:
  • Find the derivative of the function using the definition of derivative. f(x) = 1 5 x − 1 6
    8·1 answer
  • Math question down below
    15·1 answer
  • HELP, WILL GIVE BRAINLIEST!!
    9·1 answer
  • Caleb's goal is to find a job that provides an income of at least $70,000 a year. Vanessa's Furniture offers him a job paying a
    9·1 answer
  • Dale made a model of a lighthouse using a 4 inches=50 feet if the lighthouse is 120 feet tall, how tall is his model
    8·1 answer
  • What percent is 14 out of 18
    14·1 answer
  • If h(x) = 5 x and k(x)=1/x, which expression is equivalent to (koh)(x)?
    15·2 answers
  • Wit h one is greater
    9·1 answer
  • If the output and input of a linear equation are proportional, where will the graph of the equation cross the x-axis?
    9·1 answer
  • Goal: create a budget meal for a day
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!