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
Type the correct answer in the box.
Pepsi [2]

Answer:

f(g(-64)) = -190

Step-by-step explanation:

The functions are not well written.

Let us assume;

f(x) = x+1

g(x) = 3x+1

f(g(x)) = f(3x+1)

Replace x with 3x+1 in f(x)

f(g(x)) = (3x+1) + 1

f(g(x)) = 3x + 2

f(g(-64)) = 3(-64) + 2

f(g(-64)) = -192+2

f(g(-64)) = -190

<em>Note that the functions are assumed but same method can be employed when calculating composite functions</em>

8 0
2 years ago
Can you help me by showing work on some of them please I’m having trouble
Xelga [282]
1, 1.84+2= 1.84+2.00=3.84
3, 0.90+2= 0.90+2.00 = 2.90
4, 0.5+5= 0.5+5.0=5.5

Do you want more?
6 0
3 years ago
A student got 68% of the questions correct on the Social Studies test. If there were 50 questions, how many questions did they g
kaheart [24]

Answer:

The answer is 34.

8 0
3 years ago
Read 2 more answers
Somebody help me please because i’m stuck
worty [1.4K]

The question is asking for you to plug in each number in the brackets into x and solve for y, or f(x), g(x), etc. I will do no. 19 as an example:

f(x) = -3x + 1

This problem has the domains -2, -1, and 0. First, we'll start with -2:

f(x) = -3(-2) + 1

f(x) = 6 + 1

f(x) = 7

Now -1:

f(x) = -3(-1) + 1

f(x) = 3 + 1

f(x) = 4

Lastly, 0:

f(x) = -3(0) + 1

f(x) = 0 + 1

f(x) = 1

For question 23, we can use the distance formula, which is ratextime. The domain in this case is time (t). You can set up a function like this: d(t) = 60t

8 0
3 years ago
What is the constant term in the expression 6 x 3^y + 8x^2 + 5x + 7
serious [3.7K]

Answer:

The constant term is 7

4 0
2 years ago
Read 2 more answers
Other questions:
  • (x+6)(x+4)(x-3) expand and simplify
    9·2 answers
  • 5 Connie is working to earn $200. She earns
    5·2 answers
  • You but 125 tickets to an amusement park the each cost $19.50. What is the total cost of the 125 tickets
    15·1 answer
  • HELPPPPP !!!!! Answers ????
    9·2 answers
  • Suppose you want to solve the equation 2a+b=2a, where a and b are nonzero real numbers. describe the solution.
    8·1 answer
  • Brainliest for whoever gets this right!
    7·2 answers
  • Ken wants to buy two shirts. The original price of the first shirt is $34, and the original price of the second shirt is $28. Ke
    15·2 answers
  • Find the value of x if P Q R S spaceis a parallelogram.
    15·1 answer
  • What is the equation for these tables.
    8·1 answer
  • Find the gradient of the tangent to the curve y = (√x + 3)(3√x - 5) at the point where x = 1​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!