Representing numbers: Roman numerals

Representing numbers: Roman numerals

Lessons

In this lesson, we will learn:

  • How to read and write Roman Numerals using addition and subtraction

Notes:

  • The numbers we see in math are called “Western Arabic” numerals (using the digits 0 to 9)
    • The ancient Romans used a different set of numerals—Roman Numerals
    • There is NO Roman Numeral for zero
    • We still see and use Roman Numerals (i.e. naming chemical compounds, royal names, on some clocks and buildings, in laws and contracts)

  • Roman Numerals use 7 alphabetic letters as symbols to represent thousands of numbers:

Representing Numbers: Roman Numerals
    • You can use the mnemonic to help you memorize: IVy’s XL CD-roMs
    • Roman Numerals only represent the digits 1 and 5 (in different place values)

  • You read Roman Numerals from left to right and calculate the value by addition or subtraction.
    • Use addition if your values are decreasing OR repeating (big to small)
      • ex. XXVIII = 10 + 10 + 5 + 1 + 1 + 1 = 28
        • REPEATING only happens for symbols that represent a “1” digit (only I, X, C, and M are repeated)
        • Symbols can only repeat 3 times maximum (only one exception: 4000 = MMMM)

    • Use subtraction if your values are increasing (small to big)
      • ex. IV = 1 then 5 is increasing; subtract = (5 – 1) = 4
      • ex. IX = 1 then 10 is increasing; subtract = (10 – 1) = 9
        • Note that Roman Numerals only use subtraction when there is a digit of 4 or 9

  • Notice that:
Representing Numbers: Roman Numerals
    • For 1,2,3 digits: use the same power of ten symbol and repeat them
    • For 4 and 9 digits: use subtraction to calculate the value
    • For 5 digits: introduces a new symbol
    • For 6,7,8 digits: use the power of 5 symbol, then write the power of ten symbol and repeat (just like for 1,2,3 digits)
  • Introduction
    Introduction to Roman Numerals:
    a)
    What are Roman Numerals and what symbols are used to write them?

    b)
    How do you add the values of Roman Numerals?

    c)
    How do you subtract that values of Roman Numerals?

    d)
    Review of Roman Numerals and understanding patterns


  • 1.
    Roman Numeral Basics - Practice Writing
    Write the roman numerals for:

    a)
    For the ones place value (from 1 to 10)

    b)
    For the tens place value (from 10 to 100; skip counting by 10)

    c)
    For the hundreds place value (from 100 to 1000; skip counting by 100)


  • 2.
    Roman Numeral Problem Solving Riddle
    What is the longest roman numeral (the most letters)? Out of all the numbers between 1-1000?

  • 3.
    Converting Roman Numerals into Standard Form Numbers
    Write each Roman numeral as a number in standard form. Show all your work for the addition/subtraction of the values.

    a)
    XXXIX

    b)
    XLVI

    c)
    DLXXXVII

    d)
    CCXIX

    e)
    MCDLXIII

    f)
    MMMDCCLII


  • 4.
    Converting Numbers into Roman Numerals
    Write each number as a Roman numeral. Show all your work for representing the addition/subtraction of the values.

    a)
    23

    b)
    98

    c)
    461

    d)
    750

    e)
    1239

    f)
    4758


  • 5.
    Using Roman Numerals to Solve Trivia Questions
    Solve for the Roman numerals' value to find out the answer to the history fact!

    a)
    In what year did the first two humans, Neil Armstrong and Buzz Aldrin, land on the moon? In the year: MCMLXIX

    b)
    When was the first car invented? In the year: MDCCCLXXXVI

    c)
    When was the first airplane invented? In the year: MCMIII

    d)
    When was the first modern computer invented and created? Between the years MCMXXXVI and MCMXLVIII