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Decimals in Expanded Notation

Decimals in Expanded Notation. Coach Lesson 3 Also 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.

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Decimals in Expanded Notation

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  1. Decimals in ExpandedNotation • Coach Lesson 3 • Also see textbook pages 102 – 105. • Jeff Rhodus • 6th Grade • Elsanor Elementary

  2. 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 + 2/100 or 30 + 6 + 0.8 + 0.02 You can use a place-value chart to write numbers in expanded form.

  3. 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 8 5 1 Step 2: Write the value of the digit in the greatest place. 7 tens equals 70

  4. 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 + 1 70 tens plus 1 ones equals 71 Step 4: Continue for the remaining numbers. 70 + 1 + 0.8 + 0.05 70 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

  5. 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. . Tens Ones Tenths Thousandths Hundreds Hundredths 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 680 600 + 80 = 680

  6. 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 or 600 + 80 + 9/10 + 1/1000

  7. 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 ____________________.

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