What is Decimal places? — Mathematics

Definition 29.1 Primary & Middle School Mathematics · Chapter 29 — Decimal Numbers

After the decimal point come the tenths, the hundredths, the thousandths — each worth ten times less than the one before:

4.362 = 4 + \frac{3}{10} + \frac{6}{100} + \frac{2}{1000} = \frac{4\,362}{1000}.

The place-value table of 4.362: whole part in blue, decimal part in red, the point between units and tenths. — The place-value table of $4.362$ : whole part in blue, decimal part in red, the point between units and tenths.

Zooming on the number line: the stretch from 4.3 to 4.4, magnified, is itself cut into ten hundredths — and 4.362 sits just past 4.36. — Zooming on the number line: the stretch from $4.3$ to $4.4$ , magnified, is itself cut into ten hundredths — and $4.362$ sits just past $4.36$ .

Examples

Example 29.2 (Many readings, one number)

$4.362$ can be read “four point three six two”, or “four and $362$ thousandths”, or decomposed as $4 + 0.3 + 0.06 + 0.002$ . And padding with final zeros changes nothing: $4.362 = 4.3620$ . But $4.362 \neq 4.0362$ : a zero inside pushes every digit to a smaller place.

Example 29.3 (Where is it on the line?)

To place $4.362$ : between $4$ and $5$ ; zooming, between $4.3$ and $4.4$ ; zooming again, between $4.36$ and $4.37$ , closer to $4.36$ . Each decimal digit is one more level of zoom.

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Definition 38.1 Primary & Middle School Mathematics · Chapter 38 — Decimal Numbers

A decimal number has a whole part and a decimal part, separated by the decimal point. Each place to the right of the point is worth ten times less than the one before: tenths, hundredths, thousandths. For instance

13.407 = 13 + \frac{4}{10} + \frac{0}{100} + \frac{7}{1000} = 1 \times 10 + 3 + 4 \times \frac{1}{10} + 7 \times \frac{1}{1000}.

The place-value table of 13.407: the decimal point sits between the units and the tenths. — The place-value table of $13.407$ : the decimal point sits between the units and the tenths.

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Examples

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