Math Lesson 1.1.5 - Hindu-Arabic Numerals

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Welcome to our Math lesson on Hindu-Arabic Numerals, this is the fifth lesson of our suite of math lessons covering the topic of Numbering Systems, a Historical View, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Hindu-Arabic Numerals

These are numerals we actually use in a lot of activities. Hindu-Arabic is a numbering system containing 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (so it is a decimal system). Despite originally being invented in India, it was brought into Europe by Arabs during the Middle Ages.

Numbers in the Hindu-Arabic numbering system are written using the combination of the above digits. The value of these digits increases by 10 times when moving one position to the left. The rightmost digit of a Hindu-Arabic number shows the units (ones), then the next digit shows tens, then hundreds, and so on. For example, the leftmost digit in the number 44 indicates 4 tens, while the rightmost one indicates 4 ones (or units). Look at the example below.

Math Tutorials: Numbering Systems, a Historical View Example

Example 1

  1. Convert the following Roman numbers to Hindu-Arabic ones:
    CCLXXVIII =
    MCMXLIV =
    MMCDXXXIX =
    LVIDCCCXVI =
  2. Convert the following Hindu-Arabic numbers into Roman ones:
    94 =
    463 =
    3413 =
    4102 =

Solution 1

  1. We have for the first number CCLXXVIII = 278 because CC = 200; LXX = 70 and .
    For the second number we have MCMXLIV = 1944 because M = 1000; CM = 900; XL = 40 and IV = 4.
    For the third number we have MMCDXXXIX = 2439 because MM = 2000; CD = 400; XXX = 30 and IX = 9.
    For the fourth number we have LVIDCCCXVI = 56 816 because LVI = 56 000; DCCC = 800; X = 10 and VI = 6.
  2. For the first number we have 94 = XCIV because XC = 90 and IV = 4.
    For the second number we have 463 = CDLXIII because CD = 400; LX = 60 and III = 3.
    For the third number we have 3413 = MMMCDXIII because MMM = 3000; CD = 400; X = 10 and III = 3.
    For the fourth number we have 4102 = IVCII because IV = 4000; C = 100 and II = 2.

More Numbering Systems, a Historical View Lessons and Learning Resources

Arithmetic Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
1.1Numbering Systems, a Historical View
Lesson IDMath Lesson TitleLessonVideo
Lesson
1.1.1Egyptian Numerals
1.1.2Babylonian Numerals
1.1.3Mayan Numerals
1.1.4Roman Numerals
1.1.5Hindu-Arabic Numerals
1.1.6Classes and Placeholders

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