This method will instruct you to write the answer reading from left to right.
1. To change a number from base 10 to base b you must find the largest power of b that will go into the number, and write down the number of times it will go into it. (*Remember that there can be no digit in the number greater than the base.)
Ex [1] 475 = _________6.
a. In this example 63 is the largest power and it evaluates to 216, which goes into 475, 2 times. Write down 2.
2. To find the next numbers, multiply the power found in the previous step and the number of times it goes into the number. Then, subtract this value from the original number. Then find out how many times the next power goes into this number and write it down.
Ex [1] 475 = _________6.
b. Multiply 63 x 2 which equals 432. Subtract this value from 475 which equals 43. The next power in line is 62 which is 36. Since 36 goes into 43, 1 time, write down 1.
3. Repeat step 2 until all powers are gone.
Ex [1] 475 = _________6.
c. Multiply 62 x 1 which equals 36. Subtract this value from 43 which equals 7. The next power in line is 61 which is 6. Since 6 goes into 7, 1 time, write down 1.
d. Multiply 61 x 1 which equals 6. Subtract this value from 7 which equals 1. Since 60 is the last power we just write down whatever number is left, which in this case is 1.
e. The answer is 2111.
Ex [2] 134 = _________5.
a. The largest power of 5 that goes into 134 is 53 which equals 125. Since 125 only goes into 134, 1 time, we write down 1.
b. Multiply 53 x 1 which equals 125 and subtract this value from 134 which equals 9. The next power in line is 52 which is 25. Since 25 goes into 9, 0 times, we write down 0.
c. Multiply 52 x 0 which is 0 and subtract this value from 9 which is still 9. The next power in line is 51 which is 5. Since 5 goes into 9, 1 time, we write down 1.
d. Multiply 51 x 1 which is 5 and subtract this value from 9 which is 4. Since 50 is the last power we just write down
e. The answer is 1014.
Ex [3] 76 = _________2.
a. The largest power of 2 is 26 which is 64. 64 goes into 76, 1 time, so write down 1.
b. 76 - 64 = 12. The next power in line is 25 which equals 32. Since 32 does not go into 12, write down 0.
c. The next power in line is 24 which is 16. Since 16 does not go into 12, write down 0.
d. The next power in line is 23 which is 8. Since 8 goes into 12, 1 time, write down 1.
e. 12 - 8 = 4. The next power in line is 22 which is 4. Since 4 goes into 4, 1 time, write down 1.
f. 4 - 4 = 0. The next power in line is 21 which is 2. Since 2 goes into 0, 0 times, write down 0.
g. 0 - 0 = 0. Since the last power is 0, we just write down what is left, which is 0.
h. The answer is 1001100.