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
Please help ASAP!!!!!!
erica [24]

Answer:

300

Step-by-step explanation:

20*30=600

600/2=300

Please mark as Brainliest! :)

Have a nice day.

6 0
3 years ago
2. How can Diego package all the 64 cookies so that each bag has the same number of them? How many bags can he make, and how man
Readme [11.4K]
Divide 64 by multiple numbers, and if they divide evenly that’s how many will be in each bag for the number of bags (number you divided by). For example, dividing 64 by 8 (bags) would be 8 cookies in each bag. You can do this with multiple numbers as long as it goes in evenly
7 0
3 years ago
Which pair of angles is congruent by ASA?
pogonyaev

Answer:

C

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
I really need help <br> Dz,2 of X is<br> (0-4)<br> (2,-2)<br> (6,2)
kvv77 [185]

9514 1404 393

Answer:

  (6,2)

Step-by-step explanation:

As is often the case with multiple-choice problems, you don't actually need to know the detailed working. You just need to know what the answer looks like.

When point X is dilated by a factor of 2 with point Z as the center of dilation, it will move to a location twice as far from Z. You can tell by looking at the graph that X' will be in the first quadrant, above and to the right of the location of X. The only sensible answer choice is ...

  X' = (6, 2)

_____

<em>Additional comment</em>

X is a distance of X-Z = (4, 0) -(2, -2) = (2, 2) from Z Doubling that will put the image point a distance of 2(2, 2) = (4, 4) from Z. When this is added to Z, we find ...

  X' = Z + (4, 4) = (2+4, -2+4) = (6, 2)

8 0
3 years ago
PLSS HELP IMMEDIATELY!!!! ILL MARK BRAINIEST IF U DONT LEAVE A LINK OR GUESS!!!!!
jeyben [28]

Answer:

the volume will be 56 m³

because it is made of 56 cubes of 1m ³ volume

I hope it helps

7 0
3 years ago
Read 2 more answers
Other questions:
  • Suppose you have the 26 letters of the alphabet on separate cards in a hat. You pick out a card, write down the letter, put the
    7·2 answers
  • Mr. Matthews purchases 22 boxes of pencils for 4th grade classes each box contains 45 pencils how many pencils will each class r
    13·2 answers
  • Consider the graph of the linear equation 2x-5y=10. What is the x intercept?What is the y intercept?What is the slope?
    12·1 answer
  • One pair of twin primed between 1 and 6 is....
    8·1 answer
  • How many decimal places does an irrational number have?
    9·1 answer
  • A factory makes orange paint by mixing red paint and yellow paint in the ratio 7:2. The factory makes 2700 litres of orange pain
    11·1 answer
  • On a map, 1 inch = 4.5 miles. The distance between city A and city B on the map is 6 inches. How far apart are the two cities in
    15·1 answer
  • Sarah's teacher wrote this expression on the whiteboard. Where could she place brackets in the expression for it to be equal to
    13·1 answer
  • Anyone alive I need this answer
    14·1 answer
  • What is an equation of the line that passes through the points(-1,1) and (-2,-4)?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!