Procedure: How to Multiply a Decimal by a Whole Number
Multiplying a Decimal by a Whole Number is a Grade 5 math procedure from Illustrative Mathematics Chapter 5 (Place Value Patterns and Decimal Operations) where students multiply by ignoring the decimal point, then count the decimal places in the decimal factor and place the decimal point in the product accordingly. This shortcut treats decimal multiplication as whole-number multiplication followed by a place-value adjustment.
Key Concepts
To multiply a decimal by a whole number: 1. Multiply the numbers as if they were whole numbers, ignoring the decimal point. 2. Count the number of decimal places in the decimal factor. 3. Place the decimal point in the product so it has the same number of decimal places as the decimal factor.
Common Questions
How do you multiply a decimal by a whole number?
Multiply the numbers as if they were whole numbers (ignore the decimal point). Then count the decimal places in the decimal factor and place the decimal point in the product so it has that same number of decimal places.
What is an example of multiplying a decimal by a whole number?
To calculate 3.14 × 5: multiply 314 × 5 = 1570. Since 3.14 has 2 decimal places, the product is 15.70. To calculate 0.07 × 4: multiply 7 × 4 = 28. Since 0.07 has 2 decimal places, the product is 0.28.
What chapter covers decimal multiplication in Illustrative Mathematics Grade 5?
The procedure for multiplying a decimal by a whole number is covered in Chapter 5 of Illustrative Mathematics Grade 5, titled Place Value Patterns and Decimal Operations.
Why does the product of a decimal and a whole number have the same decimal places as the decimal factor?
The decimal places represent the place value of the decimal (tenths, hundredths, etc.). Multiplying by a whole number scales the amount but doesn't change how many decimal subdivisions there are.
How do you handle a zero placeholder when multiplying decimals?
If the whole-number product has fewer digits than needed for the decimal places, add a zero placeholder on the left. For example, 7 × 4 = 28, and 0.07 × 4 = 0.28 (one zero added to give 2 decimal places).