Math Problem Statement

Convert 3183 to a numeral in base 5

Solution

To convert 3183 from base 10 (decimal) to base 5, we follow these steps:

  1. Divide the number by 5, keeping track of the quotient and remainder.
  2. Continue dividing the quotient by 5 until the quotient becomes zero.
  3. The base 5 numeral will be the remainders read in reverse order.

Let's begin:

3183÷5=636 remainder 33183 \div 5 = 636 \text{ remainder } 3 636÷5=127 remainder 1636 \div 5 = 127 \text{ remainder } 1 127÷5=25 remainder 2127 \div 5 = 25 \text{ remainder } 2 25÷5=5 remainder 025 \div 5 = 5 \text{ remainder } 0 5÷5=1 remainder 05 \div 5 = 1 \text{ remainder } 0 1÷5=0 remainder 11 \div 5 = 0 \text{ remainder } 1

Reading the remainders from bottom to top, we get: 10021351 0 0 2 1 3_5.

Thus, the base 5 representation of 3183 is 100213.

Would you like further details or explanations?

Here are 5 related questions for practice:

  1. Convert 512 from base 10 to base 5.
  2. How would you convert a base 5 number back to base 10?
  3. What is the base 7 equivalent of the decimal number 3183?
  4. How can you quickly check if a base conversion was done correctly?
  5. What is the largest number that can be represented with three digits in base 5?

Tip: When converting from base 10 to any other base, always remember to read the remainders from bottom to top for the correct result.

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Math Problem Analysis

Mathematical Concepts

Number Systems
Base Conversion

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8