# Expanded Form of Numbers Worksheets

How Does Place Value Relate to The Expanded Form of Numbers? Place value is an important concept in mathematics. It is one of the first major concepts the kids are taught in school when studying numbers and counting. It helps in laying the grounds for understanding the expanded form of numbers. Every digit in a number sits in a unique position and holds value. Together these digits make up the value of the number. The smallest place value is the unit place. To understand place value, take the example of the number; 1,243. 1: 1 in the number sits at the thousand's place. 2: 2 in the number sits on the hundred's place. 4: 4 in the number sits in ten's place. 3: 3 in the number sits on the unit place. According to the place value, there are one thousand, two hundreds, four tens, and three ones that are adding to make the number 1,243. The place value helps in writing a number in its expanded form. Now that we have understood the place values of all digits in the number 1,243, we can write it down in an expanded form; 1,243 = 1,000 + 200 + 40 + 3 These worksheets display to students how to relate place value to the expanded number form.

### Aligned Standard: Grade 2 Base Ten - 2.NBT.3

- Step-by-step Lesson- This one focuses the three main place values of this standard. I use the column method again.
- Place Value and Writing Numbers in Words 5 Pack- Tell the value of the place of the underlined number.
- Writing Numbers in Word Format Pack- Write all the numbers in word format.
- Guided Lesson -We work on number names, expanded to numeric form, and writing expanded form.
- Guided Lesson Explanation - I like the way I ended up explaining these problems. Let me know if I did a good job.
- Practice Worksheet - You are given an integer in numeric form. You need to convert it to both expanded and word form.
- Matching Worksheet - Match the expanded and place value forms of numbers.
- Open Ended Integer Problems Five Pack of Worksheets - This is only for very advanced students. A teacher requested this for her gifted class. I'd say it is more of a 4th grade skill.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Tell the place value of the underlined integer, compare number, and write them in expanded form.

- Homework 1- Write the value of the underlined number. You can also write it in words for it to make sense.
- Homework 2-Identify the numbers that are less than 485? There is a series of six values to decide from.
- Homework 3- What is the expanded form of 251? You will break it down based on the example.

### Practice Worksheets

We ask you everything from the homework in one pass here.

- Practice 1- Find the final value of the following problems. All the problems are mixed up.
- Practice 2- Identify the numbers that are less than 258 from all the different choices that are available.
- Practice 3- What is the expanded form of 369? Start there and see where it goes.

### Math Skill Quizzes

For some reason students find the expanded form of numbers to be the most difficult in this section.

- Quiz 1- 198 Write the value of the underlined number?
- Quiz 2- 759 Write the value of the underlined number?
- Quiz 3- What is the expanded form of 123?

### What Is the Expanded Form Of Numbers (ex. 1,487 = 1,000 + 400 + 80 + 7)?

To understand the expanded form of a number, a child must have a clear understanding of the concept of place values of digits. Every digit in a number has a value that is determined by its position in the number. The lowest place value is the unit's place.

**Let's take the number 1,487 as an example.**

1: 1 sits at the thousand's place which means there is one thousand in the number

4: 4 sits at the hundred's place which means there are four hundred in the number

8: 8 sits at the ten's place which means there are eight tens in the number

7: 7 sits at the unit's place which means there are seven ones in the number

Now we know the numbers that are adding together to form the number 1,487. We can numerically write the information as;

1,000 + 400 + 80 + 7 = 1,487

When you know the place value of every digit in the number, you can very easily write it in an expanded form.

### When to Use Expanded Form

We will often start to learn different ways to express values. We begin by learning standard form which is the number notation that we have all been using since we learned to count. As we progress with our math skills we will learn about decimal form and as we get more involved with the base ten system, it makes sense to break things down into the base ten system. When we place values in this form it makes it easy to understand the values in each place. Breaking it up in this fashion makes it easy to comprehend the significance of each digit found within the number. In the real world many financial situations call for this. Just think about the store owner who needs to make sure they have enough change for their customers for the entire day. They need to know how many of each type of bill denomination that they need to complete their day. This is often used in the scientific communities to explain dosages and amounts of substances.

While we are on the topic of science, you may also come across a method called expanded notation for explaining the significance of a value. This differs from expanded form because it expresses the sum as a mixture of products and sums. For younger students, notation is often more difficult. Here is an example of the difference stating the value 729.

**Expanded form: 729 = 700 + 20 + 9**

**Expanded notation: 729 = (7 x 100) + (2 x 10) + (9 x 1)**