Math Problem Statement

Write 110 (in base 3) in the base-ten system.

Solution

The question asks to convert the number 1103110_3 (in base 3) to its base 10 equivalent.

Let's break this down:

Step-by-step conversion of 1103110_3:

The base-3 number 1103110_3 can be expanded as:

1103=1×32+1×31+0×30110_3 = 1 \times 3^2 + 1 \times 3^1 + 0 \times 3^0

Now calculate each term:

  • 1×32=1×9=91 \times 3^2 = 1 \times 9 = 9
  • 1×31=1×3=31 \times 3^1 = 1 \times 3 = 3
  • 0×30=0×1=00 \times 3^0 = 0 \times 1 = 0

Adding these up: 9+3+0=129 + 3 + 0 = 12

Thus, 1103110_3 in base-10 is 1212.

Would you like more details or explanations? Here are five related questions for practice:

  1. Convert 2103210_3 to base 10.
  2. Convert 1023102_3 to base 10.
  3. How would you convert a number from base 10 to base 3?
  4. What is 120131201_3 in base 10?
  5. Convert 2223222_3 to base 10.

Tip: When converting from any base to base 10, expand the number by multiplying each digit by the base raised to the power of its position (starting from 0 on the right).

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Math Problem Analysis

Mathematical Concepts

Base Conversion
Number Systems

Formulas

Base-n to Base-10 Conversion Formula: digit × base^position

Theorems

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Suitable Grade Level

Grades 5-7