Multiplying and Dividing by Powers of 10
To multiply a whole number by a power of 10 add on as many 0’s as the power. Or, you can think of it as moving the decimal point one place to the right for every power of 10 you are multiplying by.
Example 1:
87 x 10 = 870 Add on 1 zero because you are multiplying by 10 (10 has 1 zero)
87 x 100 = 8,700 Add on 2 zeros because you are multiplying by 100 (100 has 2 zeros)
87 x 1,000 = 87,000 Add on 3 zeros because you are multiplying by 1,000 (which has 3 zeros)
To divide a whole number by a power of 10 move the decimal point left as many places as there are 0’s in the power.
Example 1:
63.9/10 = 6.39 Move the point one place left.
63.9/100 = .639 Move the point two digits left.
63.9/1,000 = .0639 Move the point three digits left. To do this, add on a 0.
Note: the digits do not change when you multiply or divide by a power of 10. Only the decimal point changes place. If you multiply by a power of 10, the decimal point moves to the right.
If you divide by a power of 10, the decimal point moves to the left.
Guided Practice:
1. 851.38 x 10 = ?
2. 963.4 x 100 = ?
3. 657.9 x 1,000 = ?
4. 328.7/10 = ?
5. 961.85/100 = ?
6. 432.616/1000 = ?
7. If you trade in 5 one-hundred dollar bills in for pennies, how many pennies would you have?
8. If there are 313.9 million people in the U.S. and 10% of them own a cat, how many pet cats are there in the U.S.?
9. Robert gets paid $10.00 per hour to shovel snow. How much will he make if he shovels for 72 hours this winter?
A man named Joseph King built a model of the Eiffel Tower using only toothpicks. His tower used 110,000 toothpicks. How can we use powers of 10 to write 110,000?