Math Problem Statement

16base 9

Solution

To convert the number 1616 from base 99 to base 1010, we follow the process of evaluating the base 99 number using its positional values.

Step-by-Step Conversion

  1. Identify the digits and their positions: The number 1616 in base 99 has two digits: 11 and 66. In base 99, the rightmost digit represents 909^0, the next represents 919^1, and so on.

  2. Calculate the decimal (base 10) value: 16base 9=1×91+6×9016_{\text{base } 9} = 1 \times 9^1 + 6 \times 9^0 Calculate each term: =1×9+6×1= 1 \times 9 + 6 \times 1 =9+6= 9 + 6 =15= 15

Result

So, the number 1616 in base 99 is equal to 1515 in base 1010.

Would you like more details or have any questions? Here are some related topics:

  1. How to convert other base 99 numbers to base 1010?
  2. How to convert base 1010 numbers to base 99?
  3. Explanation of positional values in number systems.
  4. How do base systems work for bases larger than 1010 (like base 1616 or base 2020)?
  5. Practical applications of base 99 or other non-decimal bases.

Tip: When converting from any base to decimal, multiply each digit by the base raised to the power of its position, starting from 00 on the right.

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Math Problem Analysis

Mathematical Concepts

Number Systems
Base Conversion

Formulas

n_base = digit * base^position

Theorems

Positional Notation Theorem

Suitable Grade Level

Grades 5-7