Page 74 - Basic College Mathematics with Early Integers

SE CT I O N 1. 6 I MULTIPLYING WHOLE NUMBERS AND AREA 51

Concept Check Find and explain the error in the following multiplication
problem.
102
* 33
306
306
612

Objective Multiplying by Whole Numbers Ending in Zero(s)

Interesting patterns occur when we multiply by a number that ends in zeros. To see
these patterns, let’s multiply a number, say 34, by 10, then 100, then 1000.
1 zero
b
#
34 10 = 340 1 zero attached to 34.
2 zeros
#
#
34 100 = 3400 2 zeros attached to 34.
3 zeros
#
#
34 1000 = 34,000 3 zeros attached to 34.
These patterns help us develop a shortcut for multiplying by whole numbers ending
in zeros.

To multiply by 10, 100, 1000, and so on,
Form the product by attaching the number of zeros in that number to the
other factor.
#
For example, 41 100 = 4100.
3
2 zeros

Examples Multiply. PRACTICE 6–7
Multiply.
#
6. 176 1000 = 176,000 Attach 3 zeros.
6. 75 100
3 #
#
#
7. 2041 100 = 204,100 Attach 2 zeros. 7. 808 1000
3
Work Practice 6–7
We can use a similar format to multiply by any whole number ending in zeros.
For example, since

# #
#
15 500 = 15 5 100,
we find the product by multiplying 15 and 5, then attaching two zeros to the
product.
Answers
6. 7500 7. 808,000
2
15 15 500=7500 Concept Check Answer
#
* 5 102
75 * 33
306
3060
3366