Decimal Place Value
Explained w/ 19 Examples!

Have you ever wondered, “what’s the purpose of knowing decimal place value?”

Place value helps us to understand the order and meaning of a number.

It helps us to recognize the “worth” of different digits inside a given number.

For example, let’s consider the following numbers:

• 2.04
• 420

Both numbers have the same three digits but have strikingly different values.

Imagine these numbers representing how much money someone will give you, either $2.04 or $420.

Wouldn’t you want the larger amount?

Me too!

That’s why it’s important to know and appreciate place value because where a digit appears in the number determines its worth.

Place Value Chart

The best way to understand place value for decimals is to look at the following chart:

Please note that a digit in one place represents ten times as much as it represented in the place directly to its right. Additionally, that same number is one-tenth as much as the number directly to its left as noted on SplashLearn.

In other words, the place value of a digit:

1. Increases by “ten times” as we move left through the chart.
2. Decreases by “ten times” as we move right through the place value chart.

Notice that the values to the left of the decimal point represent the whole number portion of the number, and the values to the right of the decimal point represent the fractional part.

Expanded Notation With Decimals

To better understand the importance of worth, we can write numbers in expanded form. All we have to do is break up or separate a number according to its place value and write it as the sum of all the values.

For example, let’s take the numbers “84.56” and “123.456” and write them in expanded form. The solutions are seen in the two examples below.

The expanded form helps clarify the value and importance each digit plays within the number.

Writing Decimals In Standard Form

Also, we can take a number from an expanded form and write in standard decimal form. For example, let’s imagine we were asked to determine the number that is represented by 20 + 0.1 + 300 + 0.004 + 5.

We start by placing each number in order of value, making sure to line up decimal points, and then adding each number to find the sum. The example below shows how this works.

So, our standard decimal answer is 325.104.

How Do You Write A Decimal In Word Form?

Additionally, we will need to translate each decimal number to English by writing the decimal form from “word form.”

Why?

While there are countless reasons for needing to know how to say and write decimal numbers, the most obvious is the ability to write a check. The second is because it’s essential to be able to express numerical values coherently.

For example, let’s say we have the following numbers:

• 12.34
• 123.4

How would you explain these two numbers to someone else?

We would translate these numbers into words and say the first means “twelve and 34 hundredths,” The second means “one hundred twenty-three and four-tenths.”

Or imagine these were monetary values so that we would say twelve dollars and 34 cents and one hundred twenty-three dollars and 40 cents, respectively.

Worksheet (PDF) — Hands on Practice

One of the best ways to learn the material is to put a pencil to paper. And that’s what these worksheets come in to play.

Practice Problems
Step-by-Step Solutions

Together, we will look at countless examples of how to write each decimal number in expanded form, standard form, translate numbers to English, translate words to numbers, and identify the place value or digit given the desired place value.

It’s going to be fun!

Place Value – Lesson & Examples (Video)

32 min

• Introduction to Video: Place Value
• 00:00:59 – Overview of place value and understanding the place value chart for decimals

• 00:05:14 – Write the decimal in expanded form (Examples #1-3)
• 00:11:51 – Write each decimal in standard decimal form (Examples #4-5)
• 00:17:08 – Translate from English to standard decimal form (Example #6-8)
• 00:22:03 – Translate from decimal form to English (Examples #9-11)
• 00:26:13 – Determine the place value of the underlined digit (Examples #12-16)
• 00:29:20 – Write the digit in the given place value (Example #17-19)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions