How do I write the base-b numeral represented by a set of base-b blocks

How do I write the base-b numeral represented by a set of base-b blocks?

The correct answer and explanation is:

To write the base-b** numeral represented by a set of base-b blocks**, follow these steps:

✅ Correct Answer:

Add the values of each type of block (based on their place value in base-b) and write the total as a numeral in base-b.

🧠 Explanation (Around 300 Words):

In any base-b number system, place value is crucial. Just like in base-10 we have ones, tens, hundreds, etc., in base-b, the values are based on powers of b:

• The rightmost block type represents b^0 = 1 (ones),
• The next represents b^1 = b (b-units),
• Then b^2 = b², and so on.

🧮 Example:

Suppose you are working in base-5 and you are given the following blocks:

• 3 blocks of 25 (which is 525^2),
• 2 blocks of 5 (which is 515^1),
• 4 blocks of 1 (which is 505^0).

To write this in base-5:

• You place the number of blocks at each power of 5:
  • 3×25=3×523 \times 25 = 3 \times 5^2
  • 2×5=2×512 \times 5 = 2 \times 5^1
  • 4×1=4×504 \times 1 = 4 \times 5^0

Write the digits from left to right, starting from the highest power:

→ 3 2 4 (in base-5)

This is the numeral 324₅, meaning: 3⋅52+2⋅51+4⋅50=75+10+4=89 (in base-10)3 \cdot 5^2 + 2 \cdot 5^1 + 4 \cdot 5^0 = 75 + 10 + 4 = 89 \text{ (in base-10)}

🎯 Summary:

To write the base-b numeral:

1. Identify how many blocks are at each place value (power of b).
2. Arrange the digits from highest to lowest place.
3. Combine the digits to form the numeral in base-b.

This method visually represents the number based on positional value, making it easier to understand non-decimal bases.