What is Place value? — Mathematics

Definition 14.1 Primary & Middle School Mathematics · Chapter 14 — Numbers up to 10 000

A number is written with the digits $0, 1, 2, \dots, 9$ . Reading from the right, the places are: units, tens, hundreds, thousands. In $3\,254$ :

3\,254 = 3 \text{ thousands} + 2 \text{ hundreds} + 5 \text{ tens} + 4 \text{ units}.

The place-value table of 3\,254, read “three thousand two hundred fifty-four”. — The place-value table of $3\,254$ , read “three thousand two hundred fifty-four”.

Examples

Example 14.2 (The zero that holds a place)

“Four thousand and seven” is written $4\,007$ : a $4$ in the thousands, a $7$ in the units, and zeros in between to keep each digit in its right place. Without them, $47$ would be a very different number!

Example 14.3 (Exchanging)

Ten units make one ten; ten tens make one hundred; ten hundreds make one thousand. So $10$ hundreds $= 1\,000$ , and $32$ tens $= 320$ : the number $320$ contains $32$ tens (not just the digit $2$ !).

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Definition 37.1 Primary & Middle School Mathematics · Chapter 37 — Whole Numbers

Our way of writing numbers uses ten digits ( $0$ to $9$ ), and the value of a digit depends on its place: in $5\,208$ , the digit $5$ counts thousands, the $2$ counts hundreds, the $0$ counts tens (there are none) and the $8$ counts units:

5\,208 = 5 \times 1000 + 2 \times 100 + 0 \times 10 + 8 .

The place-value table of 5\,208. The 0 matters: without it, the 5 and the 2 would slide into the wrong columns and the number would read 528. — The place-value table of $5\,208$ . The $0$ matters: without it, the $5$ and the $2$ would slide into the wrong columns and the number would read $528$ .

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