Multiplying decimals by multiples of 10
Multiplying decimals by multiples of 10 is a Grade 4 skill in Saxon Math Intermediate 4 Chapter 7 using the hanging zero method. Students drop the trailing zero of the multiple of 10 into the answer line, multiply the remaining digits, then place the decimal point by counting decimal places in the original number. For example, 8.50 times 30: hang the zero, multiply 850 times 3 equals 2550, then drop in the zero to get 25500, and since 8.50 has two decimal places, the answer is 255.00 dollars. Forgetting to place the decimal is the most common error.
Key Concepts
To multiply a decimal number by a multiple of 10, use the 'hanging zero' method. After you get a product, you must place the decimal point correctly. Count the number of digits after the decimal point in the original decimal number, and make sure your final answer has the same number of decimal places.
Example 1: To find the total cost of 20 items at 1.43 dollars each, multiply $1.43 \times 20$. Let the zero hang out and drop down. Then, $143 \times 2 = 286$. Since 1.43 has two decimal places, the answer is 28.60 dollars. Example 2: For $1.64 \times 30$, drop the 0 and multiply $164 \times 3 = 492$. Since 1.64 has two decimal places, the answer is 49.20 dollars.
This is the same 'hanging zero' party, but with a special guest: the decimal point! Do your multiplication just as you learned, then stop and count the decimal places in the number you started with. Your final answer must have the exact same number of places after the decimal. It ensures your dollars and cents are always on point!
Common Questions
What is the hanging zero method for multiplying decimals by 10, 20, or 30?
Write the zero from the multiple of 10 hanging to the side, drop it into the answer line first, then multiply the remaining digits normally. Finally, place the decimal point in the answer.
How do I multiply 8.50 by 30?
Hang the zero from 30. Multiply 850 times 3 equals 2550. Drop the hanging zero to get 25500. Since 8.50 has two decimal places, the answer is 255.00.
How do I determine where to place the decimal in the answer?
Count the digits after the decimal point in the original decimal number. Your answer must have the same number of decimal places.
What happens if I forget to place the decimal point?
The answer will be 10, 100, or 1,000 times too large. For example, 255.00 dollars becomes 25,500 dollars—a very different amount.
Does the hanging zero method work for multiplying by 100 or 200?
Yes. Drop both zeros into the answer line first, then multiply the remaining digits, and apply the decimal placement rule at the end.