100X100X100,bases 2 and 5
Online, “*” is used to indicate multiplication to avoid confusion with “x” as an unknown.
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If the 100 is in base 2 or 5, then
100*100*100 = 1000000
regardless of base
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To convert the number 100x100x100 to bases 2 and 5, we need to understand what bases are and how to perform the conversion.
In mathematics, bases refer to the number systems that use a specific number of symbols or digits to represent different values. The most common base is base 10, also known as the decimal system, which uses 10 digits (0-9) to represent values.
For base 2, also known as the binary system, we use only two digits, 0 and 1. Base 5, on the other hand, uses five digits, 0-4.
To convert the number 100x100x100 to base 2:
1. Start by finding the largest power of 2 that fits into the given number. In this case, it is 2^6 since 2^7 (128) is greater than 100.
2. Divide 100 by 2^6: 100 ÷ 2^6 = 1 remainder 36.
3. Repeat the process with the remainder from step 2. Now you have 36.
4. Find the largest power of 2 that fits into 36. It is 2^5 since 2^6 (64) is greater than 36.
5. Divide 36 by 2^5: 36 ÷ 2^5 = 1 remainder 4.
6. Repeat the process with the remainder from step 5. Now you have 4.
7. Continue dividing by powers of 2 until the remainder is 0.
8. The remainders, read in reverse order, form the binary representation of the number.
In this case, it is 1100100.
To convert the number 100x100x100 to base 5:
1. Start by finding the largest power of 5 that fits into the given number. In this case, it is 5^3 since 5^4 (625) is greater than 100.
2. Divide 100 by 5^3: 100 ÷ 5^3 = 1 remainder 25.
3. Repeat the process with the remainder from step 2. Now you have 25.
4. Find the largest power of 5 that fits into 25. It is 5^2 since 5^3 (125) is greater than 25.
5. Divide 25 by 5^2: 25 ÷ 5^2 = 1 remainder 0.
6. The remainders, read in reverse order, form the base 5 representation of the number.
In this case, it is 101.
Therefore, the number 100x100x100 in base 2 is 1100100, and in base 5 is 101.