Multiplying by Multiples of 10, 100, and 1,000
To multiply a whole number by a multiple of 10, 100, or 1000, multiply the basic fact (non-zero digits) first, then append all the zeros from both factors to the product. This Grade 5 math skill from Eureka Math Chapter 7 covers mental strategies for multi-digit whole number multiplication.
Key Concepts
To multiply a whole number by a multiple of 10, 100, or 1,000, you can multiply the basic fact (the non zero digits) and then append the total number of zeros from the factors to the product.
Common Questions
How do you multiply by multiples of 10, 100, or 1000?
First multiply the basic fact (the non-zero digits), then count all the zeros in both factors and append that many zeros to the basic fact product. For example, 8 times 200: basic fact is 8 times 2 equals 16, add two zeros to get 1600.
What is a basic fact in multiplication?
A basic fact is the multiplication of the non-zero digits in the numbers. For 30 times 70, the basic fact is 3 times 7 equals 21.
What is an example of multiplying 50 times 4000?
The basic fact is 5 times 4 equals 20. Count zeros: one in 50 and three in 4000 equals four zeros total. Append four zeros to 20 to get 200,000.
Why does this method work mathematically?
Each zero represents a factor of 10, so appending zeros is the same as multiplying by those powers of 10, which correctly scales the basic fact product to its proper place value.