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How to Write Decimals in Expanded Form

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  • 0:05 What Is a Decimal?
  • 0:51 Expanded Form in Decimals
  • 2:33 Expanded Form in Fractions
  • 3:06 Lesson Summary
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Lesson Transcript
Instructor: Sarah Palacios

Sarah has completed her master’s degree in Education from the University of Texas and has received her bachelors in Interdisciplinary Studies specializing in Mathematics. She graduated with honors, Magna cum Laude, from Texas A&M University. She currently holds a principal certificate, a teaching certificate for Mathematics grades 4-8, a teaching certificate for EC – 6 as a generalist, as well as an ESL certificate. She has been an elementary school teacher for the past 4 years and is passionate about educating students to the highest degree.

Decimals can be pretty confusing. In this lesson, you will learn the value of decimal places to the thousandths and how to write them in expanded form using decimals as well as fractions.

What Is a Decimal?

A decimal is a number that means part of a whole. For example, the digit, or number, in front of a decimal represents a whole number. Let's say you have one apple; we would write that as 1.0. No one has eaten any part of that apple, yet. However, if you only have half of the apple, you no longer have the whole apple, or 1 apple, you have half of the apple. And we can write that in decimal form by saying 0.5, and we can also use words by saying five tenths of the apple, and fractions by writing 5/10. There are many other fractions that work as well. They all mean the same: you only have half of the apple left.

Here is a chart showing all the decimal places to the thousandths:


Decimal Chart to the Thousandths


Expanded Form in Decimals

Writing decimals in expanded form simply means writing each number according to its place value. This is done by multiplying each digit by its place value and adding them together. Let's look at an example: 2.435. In words, we would say this as two and four hundred thirty-five thousandths. The whole number 2 is said as two, the decimal is said as 'and,' and the decimal part, which is 435, is said as a regular number: four hundred thirty-five. But since it is a decimal, we would say the last number as its place value. The last number 5 is in the thousandths place, so we must say four hundred thirty-five thousandths.

Now, how do we write that in expanded form? Remember, expanded simply means to write each digit in its given place value and add them all together. So, let's look at that same number we talked about and write it in expanded form. We do that by multiplying each number by its place value. Let's look at that chart again:


Decimal Chart to the Thousandths


The whole number 2 has a place value of 1, so we multiply 2 by 1 and put parentheses around it to separate it from the other numbers we have: (2 x 1)

Next, we have the digit 4 in the tenths place so we multiply that by 0.1: (4 x 0.1)

Next, we have the digit 3 in the hundredths place, we multiply that by 0.01: (3 x 0.01)

Finally, we have the digit 5 in the thousandths place, we multiply that by 0.001: (5 x 0.001)

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