Skip to content

Zero and Place Value

Run the Zero and Place Value MicroSim Fullscreen

About This MicroSim

This MicroSim shows one number three ways at once. The top of the screen is a place value table with four columns: thousands, hundreds, tens and ones. Each column holds one digit and the same number of colored counters. Below the table, the number appears in our everyday digits (Hindu-Arabic numerals), in a South Asian digit set you choose (Devanagari, Bengali, Tamil or the Eastern Arabic style used for Urdu), and in Roman numerals.

When a column inside the number is empty, it glows and its 0 turns orange: the zero is holding that place. Tick Hide the zeros to remove every zero symbol. The digits slide together and the number turns into a different number, which is exactly the problem a zero solves. Roman numerals never need a zero, because their letters keep the same value wherever they sit, but they get long and are hard to calculate with. (Standard Roman numerals stop at 3,999; for bigger numbers the sim simply repeats M, which is a modern shortcut rather than how Romans wrote them.)

The digit sets use real Unicode characters (U+0966 to U+096F for Devanagari, U+09E6 to U+09EF for Bengali, U+0BE6 to U+0BEF for Tamil and U+06F0 to U+06F9 for the Eastern Arabic style). Your device's fonts decide exactly how they look.

How to Use

  1. Tap or click the up arrow at the top of a column to add one to that place, or the down arrow to take one away.
  2. Build 507. Read all three rows: the table, the digits, and the Roman numeral DVII.
  3. Tick Hide the zeros. Read the warning and notice what number you seem to see now.
  4. Untick it. Use the menu to switch between Devanagari, Bengali, Tamil and Urdu digits.
  5. Press Random to get new numbers (many will have an empty place). Press Clear to start from 0.
  6. Try 3,888 and 1,000 and compare how long each Roman numeral is.

Learning Objective

Students will be able to explain why a symbol for zero makes a place value system work, by comparing the same number written in a place value table, in a South Asian digit set and in Roman numerals.

Bloom level: Understand (explain, compare).

Iframe Embed Code

<iframe src="https://aaryavvatts-lab.github.io/south-asian-culture-textbook/sims/ch16-zero-place-value/main.html" height="642px" width="100%" scrolling="no"></iframe>

Lesson Plan

Grade level: 9-12 (world history, math history, ethnic studies, or a South Asian student club meeting)

Duration: 15 to 20 minutes

Activity:

  1. (3 min) Without the sim, students write 507 in Roman numerals and try to multiply DVII by XII on paper. Discuss how hard it is.
  2. (5 min) Students build 507, 2,026 and 9,009 in the sim and record each in Devanagari, Bengali and Roman numerals.
  3. (5 min) Students tick "Hide the zeros" for each number and write down what the number seems to become.
  4. (5 min) Pairs discuss: Why didn't Roman numerals need a zero? Why does our system need one? Which system would you choose for doing taxes, and why?

Assessment questions:

  1. In the number 2,006, what places are the two zeros holding?
  2. Why does 507 turn into 57 when the zero is removed, but DVII stays DVII?
  3. Write 1,947 in Devanagari or Bengali digits.
  4. Brahmi numerals had separate signs for 10, 20 and 30. Why don't they need a zero?
  5. Explain in two sentences why historians say the zero was one of the most useful ideas in the history of mathematics.

Chapter 16: Science, Math, and Ideas