Question 18 of 21advanced🔍 AnalyzeLong Answer5 marks

Why do you think the Chinese alternated between the Zong and Heng symbols? If only the Zong symbols were to be used, how would 41 be represented? Could this numeral be interpreted in any other way if there is no significant space between two successive positions?

Correct Answer

Why the Chinese alternated between Zong and Heng symbols:

The Chinese alternated between Zong and Heng symbols to clearly distinguish between different place values without relying solely on spacing.

This alternating pattern makes it immediately clear which position a symbol occupies:

  • Zongs represent units, hundreds, tens of thousands (even powers of 10)
  • Hengs represent tens, thousands, hundreds of thousands (odd powers of 10)

If only Zong symbols were used, 41 would be represented as:

Four horizontal strokes (for 4) in the tens position One vertical stroke (for 1) in the units position

Potential misinterpretation without clear spacing:

Without clear spacing, this could be misinterpreted as other numbers because:

  • The symbols for different positions would look identical
  • It would be impossible to distinguish between:
    • 41
    • 4001
    • 410

∴ The alternating Zong-Heng system serves as a visual aid to distinguish positions, similar to how the Hindu system uses position alone.

Exercise: Figure it Out (Section 10) | Q: 1 | (Page Page 33)
For More Understanding

Explanation

The chapter explains that the Chinese rod numeral system uses Zongs for units, hundreds, tens of thousands (positions with even powers of 10) and Hengs for tens, thousands, hundreds of thousands (positions with odd powers of 10). This alternating pattern serves as a visual aid to distinguish positions, similar to how the Hindu system uses position alone. Without this alternation, ambiguity could arise in reading numbers, especially when spacing between positions is unclear.

Solution Steps

  1. Step 1: Explain that Zong and Heng symbols alternate to distinguish place values without relying solely on spacing.

  2. Step 2: Identify that Zongs represent even powers of 10 (units, hundreds, tens of thousands) and Hengs represent odd powers of 10 (tens, thousands, hundreds of thousands).

  3. Step 3: Represent 41 using only Zong symbols: four horizontal strokes in tens position, one vertical stroke in units position.

  4. Step 4: Identify ambiguity: without spacing, 41 could be misinterpreted as 4001 or 410 since symbols look identical across positions.

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