6th Grade Math Textbook, Progress

Multiplication Patterns

2-1

You can use patterns to multiply by powers and

multiples of 10.

To multiply a whole number by a power or

multiple of 10:

• Multiply the nonzero digits in the factors.


• Write one zero to the right of the product
  for each zero in the factor or factors.

1 
 34  34

10 
 34  340

100 
 34  3400

1000 
 34 34, 000

35 
 2  70

35 
 20  700

35 
 200  7000

35 
 2000 70, 000

6 
 5  30

60 
 50  3000

600 
 500  30 0,000

6000 
 5000 30,000,000

To multiply a decimal by 10, 100, or 1000:


Count the number of zeros in the

multiplier.


Move the decimal point in the multiplicand.

to the rightone place for each zero.


Write as many zeros in the product as needed

to place the decimal point correctly.

Study these examples.

10 
0.5 6 5.6 1 zero: Move 1 place to the right.

1 0 0
0.00 40.4 2 zeros: Move 2 places to the right.

1 0 0 0
2.00 32 0 0 3 3 zeros: Move 3 places to the right.

1 0 0
0.8 0 8 0 2 zeros: Move 2 places to the right.

Write 1 zero as a placeholder.

1 0 0 0
1 5.80 01 5,80 0 3 zeros: Move 3 places to the right.

Write 2 zeros as placeholders.

multiplicand

multiplier with 3 zeros

3 places to the right

Write 1 zero.

0.07


 1000

0.07 0

Power of 10:

101  10

102  100

103 1000, and so on.

Multiple of 10:

10 
 1  10

10 
 2  20

nonzero digits^10 
^3 30, and so on.

2.3

8206-2_066-067 10/12/07 6:42 PM Page 66