Writing Decimals in Expanded Form: 5th Grade Math

Learning how to write decimals in expanded form is an important skill in 5th grade math. It helps students understand the value of each digit in a decimal number and strengthens their number sense. Whether you’re working on 5th grade decimal worksheets or practicing at home, this guide will make it easy to master the expanded form of decimal numbers.

What Are Decimals in Expanded Form?

The expanded form of decimal numbers is a way to break down a decimal into the sum of its individual place values. Just like whole numbers, decimals have place values such as tenths, hundredths, thousandths, and so on. Writing decimals in expanded form helps us see how much each digit contributes to the total value of the number.

For example, the number 3.42 can be written in expanded form as:
3 + 0.4 + 0.02

Here’s how it works:

• The digit 3 is in the ones place.
• The digit 4 is in the tenths place (which means 4/10 or 0.4).
• The digit 2 is in the hundredths place (which means 2/100 or 0.02)

How to Write a Decimal in Expanded Form

Writing decimals in expanded form is simple if you follow these steps:

1. Identify the place value of each digit in the decimal number.
2. Write each digit as its place value (e.g., 0.5 for 5 tenths).
3. Add them together using a plus sign (+).

Let’s look at some examples:

Example 1: 7.63
– 7 is in the ones place: 7
– 6 is in the tenths place: 0.6
– 3 is in the hundredths place: 0.03

Expanded form: 7 + 0.6 + 0.03

Example 2: 12.508
– 1 is in the tens place: 10
– 2 is in the ones place: 2
– 5 is in the tenths place: 0.5
– 0 is in the hundredths place: 0.00
– 8 is in the thousandths place: 0.008

Expanded form: 10 + 2 + 0.5 + 0.008

Example 3: 0.924
– 0 is in the ones place: 0
– 9 is in the tenths place: 0.9
– 2 is in the hundredths place: 0.02
– 4 is in the thousandths place: 0.004

Expanded form: 0.9 + 0.02 + 0.004

Real-World Example of Decimal in Expanded Form: Money

Let’s use money to understand decimals in expanded form. Imagine you have $15.75.

• 1 is in the tens place: $10
• 5 is in the ones place: $5
• 7 is in the tenths place: $0.70 (or 70 cents)
• 5 is in the hundredths place: 0.05(or 5 cents)

Expanded form: 10 + 5 + 0.70 + 0.05= $15.75.
This shows how each part of the decimal contributes to the total amount of money.

Practice with 5th Grade Decimal Worksheets

To get better at writing decimals in expanded form, try using 5th grade math worksheets. These worksheets are designed to help you practice and master this skill. 

This interactive and printable worksheet, that aligns with the Common Core State Standards, 5.NBT.A.3.A-2, advances students’ understanding of decimal numbers through multiple representations and comparisons. The material focuses on two decimal numbers (75.8025 and 254.2154), requiring students to express them in different forms while analyzing their place values

Expanded Form of Decimal Numbers Worksheet

Decimal Games for 5th Grade

If you want to make learning more fun, try playing decimal games for 5th grade. These games make practicing decimals exciting and interactive. Look for games that focus on place value, expanded form, and comparing decimals.

Writing decimals in expanded form is a key part of 5th grade math. By breaking down decimals into their place values, you can better understand how numbers work. Use 5th grade math worksheets to practice, and don’t forget to check out decimal games for 5th grade for a fun way to learn!

Practice comparing decimals with our engaging Grade 5 Comparing Decimals Worksheets! Perfect for practicing greater than, less than, and equal to with decimals, these worksheets align with the 5.NBT.A.3 Common Core standard. 
Strengthen your understanding of decimal place value with our Grade 5 Decimal Place Value Worksheets! From tenths to thousandths, these worksheets make learning fun and easy. Aligned with 5.NBT.A.3.A

check out our other blog on decimal worksheets!

Keep practicing, and soon you’ll be a pro at writing decimals in expanded form!