# Writing Decimals in Expanded Form Worksheets

In the English language there are many ways to get across the same thought to another person. A quick example may be to pass on the thought that you are in need of a drink of water. You could just say you were thirsty. You could say you were dehydrated or simply that you needed some water. In math there are many ways to communicate the same thought. In the case of expressing the amount or quantity of a value we have already learned standard and expanded form. If we remember back, expanded form is expressing the value of each integer of a value by expressing each place value individually. When it comes to converting decimal values the same rules apply, we are now conveying the values of integers that are found to the right of the decimal point. This collection of lessons and worksheets will show us how to take a decimal value and write it in expanded form.

### Aligned Standard: Grade 5 Base Ten - 5.NBT.A.3.A

- Step-by-step Lesson- Writing it in standard form and then convert an expanded number to back.
- Guided Lesson - This lesson builds, as far as difficulty, with each question.
- Guided Lesson Explanation - There are a number of different ways to explain this. I give students two different perspectives.
- Practice Worksheet 1 - A simple string of rote problems for you.
- Practice Worksheet 2 - This sheet extended the difficulty by using higher and lower place values.

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

### Practice Worksheets

Some more practice or review sheets for those that could use the work .

- Practice 3 - Write the numbers in expanded form.
- Practice 4 - Write the numbers in standard form.

### Math Skill Quizzes

The quizzes work on similar skills. This sheets are handy to diagnose problems.

- Quiz 1 - Larger values on both sides of the decimal point can be found on the quiz.
- Quiz 2 - Slap all those expanded form values together and then break them down.

### What is the Difference Between Expanded Form and Standard Form?

When we work with math we may come across a wide range of values. How we communicate those values to other people can take on many different forms. Which way is best really depends on the situation that you find yourself in. The goal is to communicate the value with our intended audience best. The important thing to remember is that no matter which form of notation that you choose, the value remains the same. Here are the common forms of notation that you will find at this grade level:

**Standard Form** -The standard form of a value is how you simply write the decimal number in its original form with all integers intact in a straight stream. That is, in the form 54.315; where the place value of each integer can be shown in the table below. The value of every place in that value is:

5 Tens, 4 Ones, 3 Tenths, 1 Hundredths, 5 Thousandths

**Expanded Form** - The expanded form expresses the exact value of each integer in a value. They are written showing the value of each integer, but in the form of addition. The complete sum is equal to the overall value. While this may just seem like more work, this gives you an exact identity for the value that you are attempting to communicate. This is often used in many scientific recipes when there is limited laboratory equipment available. Here is an example of the same value (standard form - 54.315).

Expanded Form = 50 + 4 + 3/10 + 1/100 + 5/1000

**Scientific Notation** - There is also another way to express values that is often found in most science labs. This is more advanced version of notation, but students at this level have the necessary skills to understand and more importantly put it to use. In this format a value is expressed as a power of ten. This form is used most regularly to express very large or small values. In a way, the value appears cleaner especially is that value includes a greater number of zeroes. Here is example:

Standard = 125,000, Expanded: 100,000 + 20,000 + 5,000, Scientific Notation 1.25 x 10^{5}

Learning decimals can be difficult if not understood properly, especially if you want to learn the difference between the expanded form and the standard form. A decimal is defined as the number which is part of a whole. For example, if you eat half of your favorite chocolate bar, then you have eaten 0.5 part of it. The decimal point represents the 1/2 of the whole chocolate bar.