Question

Сравни выражения 31468(8) и 12022134(4)

Answer 1

31468(8)  больше, чем 12022134(4). Это бесконечные периодические числа, а 3 больше 1.

Answer 2

Comparing Expressions 31468(8) and 12022134(4)

When comparing the expressions 31468(8) and 12022134(4), it's important to understand the notation used. The numbers in parentheses indicate the base of the number system in which the expression is written. The first number is the actual value, and the second number in parentheses represents the base of the number system.

Expression 31468(8): This expression represents the number 31468 in base 8, also known as octal notation. In octal notation, the digits range from 0 to 7, and each digit's place represents a power of 8.

Expression 12022134(4): This expression represents the number 12022134 in base 4. In base 4, the digits range from 0 to 3, and each digit's place represents a power of 4.

To compare these two expressions, we can convert both numbers to a common base, such as base 10, to facilitate the comparison.

Converting 31468(8) to base 10: ``` 3 * 8^4 + 1 * 8^3 + 4 * 8^2 + 6 * 8^1 + 8 * 8^0 = 3 * 4096 + 1 * 512 + 4 * 64 + 6 * 8 + 8 * 1 = 12288 + 512 + 256 + 48 + 8 = 130112 ```

Converting 12022134(4) to base 10: ``` 1 * 4^7 + 2 * 4^6 + 0 * 4^5 + 2 * 4^4 + 2 * 4^3 + 1 * 4^2 + 3 * 4^1 + 4 * 4^0 = 16384 + 3072 + 0 + 128 + 32 + 16 + 12 + 4 = 19656 ```

Comparison: - The value of 31468(8) in base 10 is 130112. - The value of 12022134(4) in base 10 is 19656.

Therefore, in base 10, the value of 31468(8) is greater than the value of 12022134(4).

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