Place Value: Decimals

Decimals are a quick and easy way to write fractions and mixed numbers that have denominators that are powers of $10$ , such as $10$ , $100$ , $1000$ , and so on.

Place value

When a number has a decimal point, the first number after the decimal point (to the right of it) shows the number of tenths.

As an example, the number 0.8 is equivalent to the fraction $\frac{8}{10}$ .

The second number to the right of the decimal point shows the number of hundredths.

For instance, $5.35$ is the same thing as $\frac{535}{100}$ . It should be noted that the first number to the left of the decimal point is in the ones place.

It's possible to write decimals with as many places to the right of the decimal point as you need. For example, π has been calculated to millions of decimal places.

Let's look at a number with digits into the millionths place.

$38.294137$

In this number,

• $3$ is in the tens place
• $8$ is in the ones place
• $2$ is in the tenths place
• $9$ is in the hundredths place
• $4$ is in the thousandths place
• $1$ is in the ten thousandths place
• $3$ is in the hundred thousandths place
• $7$ is in the millionths place

Visualizing decimals

It is easy to visualize decimals using base $10$ blocks. The large square indicates one whole. Cut the square into $10$ equal strips that each equals one-tenth, or $0.1$ . Then cut each strip into $10$ squares, each of which equals one-hundredth, or $0.01$ .

Example 1

If I have $2$ big squares, $4$ strips, and $5$ blocks, what number does that represent?

The two big squares represent $2$ in the ones place, because they are two wholes. The $4$ strips indicate $4$ tenths, and the $5$ blocks indicate $5$ hundredths. So the blocks all together represent the decimal:

$2.45$

Example 2

If I have $8$ strips and $3$ small squares, what number does that represent?

There are no wholes, so there is a $0$ in the ones place. There are $8$ tenths and $3$ hundredths, so together, they represent the decimal:

$0.83$

Example 3

If I have only $6$ small squares, what number does that represent?

Because there are $0$ wholes and $0$ tenths, and only $6$ hundredths, this represents the decimal:

$0.06$

Topics related to the Place Value: Decimals

Comparing Decimals

Operations with Decimals

Adding and Subtracting Fractions with Unlike Denominators

Flashcards covering the Place Value: Decimals

5th Grade Math Flashcards

Common Core: 5th Grade Math Flashcards

Practice tests covering the Place Value: Decimals

MAP 5th Grade Math Practice Tests

Common Core: 5th Grade Math Diagnostic Tests

Get help learning about place value: decimals

Learning about place value in decimals can be confusing, in part because it goes backward compared to place value in whole numbers. If your student is struggling to understand place value in decimals, have them meet with a professional tutor. Their tutor can walk them through all the concepts and help them practice problems using their learning style. This makes for effective and efficient learning. To learn more about how tutoring can help your student understand place value in decimals, contact Varsity Tutors today and speak with one of our helpful Educational Consultants.