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Multiplication - Multiples and Powers of Ten

Quick! Count by tens in your head. Each number that you recited is referred to as a multiple of ten. By the way, regardless of how far you count, each number has a zero at the end. It may be obvious, but I needed to point this out to make a point later.
10, 20, 30, 40 . . . 110, 120. . . 450 . . . 1000, etc

Now Study: 3 x 10 =30; 4 x 10 = 40; 5 x 10 = 50 23 x 10 =230

Another way to look at this pattern is to consider what happens when you multiply by 10, 100, 1000, 10000, etc. (called powers of ten)

Now examine:
45 x 1 = 45
45 x 10 = 450
45 x 1000 = 45,000
45 x 1,0000 = 450,000

Reminder: numbers that are multiplied are called factors. The answer to a multiplication problem is called a product

Try covering up the zeros in the 2nd factor of each above equation. What do you notice? The equations all become 45 x 1. Now, look at the products. Compare the number of zeros in the product to the number of zeros in the 2nd factor. Wow! They are the same.

Therefore, I think we can agree on the following steps when multiplying numbers that end with zero(s).

Step 1) Count the number of zeros at the end of each number, and mentally drop or cover up the zeros at the end of each number.
(Now, you have what looks like a very familiar basic fact or two factors without zeros at the end.)

Step 2) Multiply the factors without the zeros.


Step 3) Write the partial product and attach the same numbers of zeros you dropped to complete the answer.



Example 1: 67 x 100 =
Step 1) Count the number of zeros at the end of each number, and mentally drop them. There are two zeros.

Step 2) Multiply the factors without the zeros 67 X 1 = 67

Step 3) Write the partial product and attach the same numbers of zeros you dropped to complete the answer. 67 x 100 = 6,700


Example 2: 120 x 300 =
Step 1) Count the number of zeros at the end of each number, and mentally drop them There are three zeros.

Step2) Multiply the factors without the zeros 12 x 3 = 36

Step 3) Write the partial product and attach the same numbers of zeros you dropped to complete the answer. 120 x 300 = 36,000


Practice:

a) 578 x 100 =
b) 49 x 10 =
c) 1,000 x 327 =
d) 30 x 50 =
e) 10,000 x 8 =
f) 20 x 400 =
g) 124 x 1,000,000 =
h) 250 x 200 =
i) 2130 x 20 =
j) 80,000 x 40 =




Answers:

a) 57,800
b) 490
c) 327,000
d) 1,500
e) 80.000
f) 8,000
g) 124,000,000
h) 50,000
i) 42,600
j) 3,200,000



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