Math Problem Statement

How would you write the following number in base 10: ๐“ฆ ๐“ก ๐“ ?

Solution

The image shows a quiz question about a base 12 numeral system, where unique symbols are used to represent digits from 0 to 11. Here is a transcription of the relevant information:

Symbols for Base 12 Numerals:

  • 0 = โต”
  • 1 = ๐“š
  • 2 = ๐“ก
  • 3 = ๐“ 
  • 4 = ๐“ท
  • 5 = ๐“ณ
  • 6 = ๐“ช
  • 7 = ๐“ฐ
  • 8 = ๐“ฉ
  • 9 = ๐“ฎ
  • 10 = ๐“ฅ
  • 11 = ๐“ฆ

Question:

"How would you write the following number in base 10?" followed by the base 12 number: ๐“ฆ ๐“ก ๐“ .

Let's break down the base 12 number to base 10:

  1. The number ๐“ฆ ๐“ก ๐“  corresponds to the digits:

    • ๐“ฆ = 11
    • ๐“ก = 2
    • ๐“  = 3
  2. Interpreting the number 11 2 3 in base 12: (11ร—122)+(2ร—121)+(3ร—120)(11 \times 12^2) + (2 \times 12^1) + (3 \times 12^0)

Now let's calculate this step-by-step.

11ร—122=11ร—144=158411 \times 12^2 = 11 \times 144 = 1584

2ร—121=2ร—12=242 \times 12^1 = 2 \times 12 = 24

3ร—120=3ร—1=33 \times 12^0 = 3 \times 1 = 3

Adding these values gives:

1584+24+3=16111584 + 24 + 3 = 1611

Conclusion:

The base 10 equivalent of the base 12 number ๐“ฆ ๐“ก ๐“  is 1611.

Would you like more details on this calculation, or do you have any other questions?

Additional Questions for Exploration:

  1. How would you convert another base 12 number, like ๐“ณ๐“ฉ๐“ฐ, to base 10?
  2. What is the process for converting from base 10 to base 12?
  3. How do you perform addition in base 12?
  4. Why might a base 12 numeral system be used historically or practically?
  5. Can you think of any other numeral systems that use bases different from 10 or 12?

Tip: When converting numbers from one base to another, break down each digit according to its place value, and use the base's power to compute the equivalent in base 10.

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Math Problem Analysis

Mathematical Concepts

Base 12 Numeral System
Place Value
Base Conversions

Formulas

(a_n * base^n) + (a_(n-1) * base^(n-1)) + ... + (a_0 * base^0)
Base 12 Place Value: 12^2, 12^1, 12^0

Theorems

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Suitable Grade Level

Grades 8-10