# Place Value: Decimals

**
Decimals
**
are a shorthand way to write
fractions
and
mixed numbers
with
denominators
that are
powers of
$10$
, like
$10,100,1000,10000,$
etc.

If a number has a
**
decimal point
**
, then the first digit to the
**
right
**
of the decimal point indicates the number of tenths.

For example, the decimal $0.3$ is the same as the fraction $\frac{3}{10}$ .

The second digit to the right of the decimal point indicates the number of hundredths.

For example, the decimal
$3.26$
is the same as the mixed number
$3\frac{26}{100}$
. (Note that the first digit to the
**
left
**
of the decimal point is the ones digit.)

You can write decimals with many places to the right of the decimal point. For example, this is a representation of the mixed number $51\frac{48053}{1000000}$ , with the place values named:

One good way to visualize decimals is by using base $10$ blocks. For instance, suppose a large square respresents one whole. If the square is cut into $10$ strips of equal size, then each of these represents one tenth or $0.1$ . Each strip can be cut into ten smaller squares to represent hundredths.

**
Example 1:
**

What number does the following set of blocks represent?

There is $1$ large square, so the ones digit is $1$ . There are $3$ one-tenths strips, so the tenths digit is $3$ . There are $6$ one-hundredth squares, so the hundredths digit is $6$ .

So, the figure represents the decimal
**
$1.36$
**
.

**
Example 2:
**

What number does the following diagram represent?

The large square is divided into
$100$
squares. Seven complete rows
have been shaded (that is, seven tenths) along with nine squares of another row (nine hundredths). So, the decimal number is
**
$0.79$
.
**

**
Example 3:
**

If the large square represents one whole, what decimal number does the diagram represent?

The large square is divided into
$100$
squares. No complete rows
have been shaded (that is, zero tenths) but four small squares of one row have been shaded (four hundredths). So, the decimal number is
**
$0.04$
**
.