What is Place Value?

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

Place value gives great versatility to our numeration system, but also makes it potentially confusing for children.

Place Value and Number Names

Hindu-Arabic Number Symbols

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:

Digits

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.

English Number Names

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.

What should teachers do?

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.

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Picture credits: Peter Price

<< Part II:   What Are Rational Numbers?

>> Part IV:   Decimal Fractions and Percents

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These notes were prepared as handouts for a conference session:

NCTM 1999 Annual Meeting – San Francisco [Visit the NCTM site]. They were previously hosted at hi-flyer.com, and were moved to Classroom Professor in April, 2010.