Decimals in Expanded Notation

Decimals in Expanded Notation

Coach Lesson 3Also see textbook pages 102 – 105.

Jeff Rhodus

6th Grade

Elsanor Elementary

Coach Lesson 3Also see textbook pages 102 – 105.

Jeff Rhodus

6th Grade

Elsanor Elementary

Getting the Idea!

A decimal is any number written with digits to the right of a decimal point.

When a number is written as the sum of the products of each digit and its place value, it is written in expanded form.

Standard form: 36.82

Expanded form: 30 + 6 + 8/10 + 2/100or

30 + 6 + 0.8 + 0.02

You can use a place-value chart to write numbers in expanded form.

Example 1:Question: What is 71.85 written in expanded form?Strategy: Use a place-value chart.

Step 1:Place each digit in the place-value chart.

Tens Ones . Tenths Hundredths

7 1 . 8 5

Step 2: Write the value of the digit in the greatest place.

7 tens equals 70

Step 3: Place an addition sign to the right of the number. Then write the value of the digit in the next greatest place.

70 + 170 tens plus 1 ones equals 71

Step 4: Continue for the remaining numbers.

70 + 1 + 0.8 + 0.0570 tens + 1 ones + 8 tenths + 5 hundredths = 71.85

Solution: The number 71.85 written in expanded form is: 70 + 1 + 0.8 + 0.05 or 70 + 1 + 8/10 + 5/100

Example 2:Question: What is 680.901 written in expanded form?

Strategy: Use a place-value chart.

Step 1: Place each digit in the place-value chart.

Hundreds Tens Ones . Tenths HundredthsThousandths

6 8 0 . 9 0 1

Step 2: Write the value of the digit in the greatest place. Place an addition sign to the right of the number. Then write the value of the digit in the next greatest place.

6 hundreds plus 8 tens equals 680600 + 80 = 680

Step 3: Continue doing this for the remaining numbers. Remember that the zeros are also place holders.

6 hundreds + 8 tens + 0 ones + 9 tenths + 0 hundredths + 1 thousandths = 680.901

Solution: The number 680.901 written in expanded form is:

600 + 80 + 0.9 + 0.001

or600 + 80 + 9/10 + 1/1000

Coached Example:Question: What is the expanded form of 42.07?Thinking It Through: What is the value of each digit?

There are ________ tens = ________.

There are ________ ones = ________.

There are ________ tenths = ________.

There are ________ hundredths = ________.

Solution: The expanded form of 42.07 is: _____________________ or ____________________.