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| Overview | Introduction to Rational Numbers | Place Value Notes |
Decimals and Whole Numbers | Software & Decimals |
Place value is the property which assigns a value to each numerical digit according to its position in the number. For example, in the number 45.209, each digit represents a specific amount. the amount depends on the position of the digit in the number, relative to the ones place:
Place value gives great versatility to our numeration system, but also makes it potentially confusing for children.
The Hindu-Arabic base-ten numeration system is based around the use of only 12 or 13 symbols (depending on the decimal point symbol, thousands marker, etc.) to show whole numbers and decimals:
A sequence of these symbols alone can stand for any one of an infinite set of different numbers. For those who understand the rules of the system, numerical symbols are an excellent way to record numbers in a way that is easy to write, easy to store electronically, completely systematic, and unambiguous.
By contrast, the names of numbers in the English language (and many other European languages) include many inconsistencies and difficulties for children. For example, the names of multiples of ten include some consistencies. For example:
| 60 | six tens | sixty |
| 70 | seven tens | seventy |
| 80 | eight tens | eighty |
The names above are consistent with the names for the single digits 6, 7, & 8, with "ty" added. On the other hand, look at these number names:
| 20 | two tens | twenty |
| 30 | three tens | thirty |
| 50 | five tens | fifty |
A consistent number naming system would use the names "twoty", "threety", and "fivety" for these numbers. The "teen" numbers introduce many other inconsistencies, including using "teen" instead of "ten", putting "teen" after the number part (e.g., "sixteen" instead of "teensix"), and using two non-teen names for 11 and 12.
Teachers of mathematics in primary and elementary classes should:
 | take special care to introduce consistently-named numbers before those that are irregular; |
| realize that while the numeration system is completely consistent, the naming system is not; |
| give students lots of practice in naming and representing numbers in a variety of ways, using a variety of physical and pictorial models. |
Go to: Decimals & Whole Numbers Notes
© Peter Price, 1999
