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# Multiply And Divide Decimals By Powers Of 10

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Learn how to multiply and divide decimals by powers of 10!

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### Multiply And Divide Decimals By Powers Of 10

1. 1. Multiply and Divide Decimals by Powers of 10 Mrs. Young EMC 1
2. 2. <ul><li>1, 10, 100, 1000, 10000, etc. are all powers of 10 </li></ul><ul><li>These numbers can be written using exponents </li></ul><ul><li>1 = 10 </li></ul><ul><li>10 = 10 </li></ul><ul><li>100 = 10 </li></ul><ul><li>1000 = 10 </li></ul><ul><li>10000 = 10 </li></ul>What are powers of 10??? 4 1 2 3 0
3. 3. What are exponents? <ul><li>An exponent tells us how many times to multiply a number by itself </li></ul><ul><li>For example </li></ul><ul><ul><li>10 </li></ul></ul><ul><ul><li>This tells us to multiply 10 x 10 </li></ul></ul><ul><ul><li>5 </li></ul></ul><ul><ul><ul><li>This tells us to multiply 5 x 5 x 5 </li></ul></ul></ul>2 3
4. 4. Powers of 10 continued… <ul><li>The fractions , , , , </li></ul><ul><li>etc… are also considered powers of ten. </li></ul><ul><ul><li>In decimal form they can be written 0.1, 0.01, 0.001, 0.0001, etc. </li></ul></ul>
5. 5. Powers of 10 practice <ul><li>1) Of the following ten decimal numbers, five are powers of 10. </li></ul><ul><li>Circle them. </li></ul><ul><li>1,000,000 10.0 100.1 </li></ul><ul><li>0.0011 20,000 1,100 0 </li></ul><ul><li>1 0.00001 0.010 </li></ul>
6. 6. Multiplying by powers of 10 <ul><li>Probably because we have ten fingers, we use a decimal system which is based on powers of 10. </li></ul><ul><ul><li>Because of this, it is easy to multiply and divide by powers of 10. To do so we only need to move the decimal place. </li></ul></ul>
7. 7. Multiply by Powers of 10 <ul><li>To multiply a number by a power of 10 like 10, 100, or 1000, we just have to move the decimal point to the right an appropriate number of places. </li></ul><ul><li>To multiply by 10 we move one place </li></ul><ul><li>To multiply by 100 we move two places </li></ul><ul><li>To multiply by 1000 we move three places and so on. </li></ul>
8. 8. Multiply by Powers of 10 <ul><li>Here are some examples: </li></ul><ul><li>1.25 x 10 = 12.5 </li></ul><ul><li>1.25 x 100 = 125 </li></ul><ul><li>1.25 x 1,000 = 1,250 </li></ul><ul><li>1.25 x 1,000,000 = 1,250,000 </li></ul>
9. 9. Multiply by Powers of 10 using exponents <ul><li>With the same examples as the previous slide, we can use exponents to multiply by powers of 10 </li></ul><ul><li>1.25 x 10 (move decimal to right once) </li></ul><ul><li>1.25 x 10 (move decimal to right two times) </li></ul><ul><li>1.25 x 10 (move decimal to right three times) </li></ul><ul><li>1.25 x 10 (move decimal to right six times) </li></ul><ul><li>**The exponent tells us how many times to move the decimal point to the right </li></ul>1 2 3 6
10. 10. Multiply by Powers of 10 <ul><li>Do some by yourself. </li></ul><ul><li>3.8 x 10 = __________ </li></ul><ul><li>3.8 x 10 = __________ </li></ul><ul><li>3.8 x 10 = __________ </li></ul><ul><li>3.8 x 10,000 = __________ </li></ul>3 7
11. 11. More difficult examples <ul><li>1,280 x 1,000 = 1,280,000 </li></ul><ul><li>0.026 x 10 = 2.6 </li></ul><ul><li>10.0036 x 1,000 = 10,003.6 </li></ul><ul><li>4.99 x 10 = 49,900 </li></ul>2 4
12. 12. Dividing by powers of 10 <ul><li>Dividing is just as easy; the decimal place simply moves to the left instead of to the right. </li></ul><ul><li>250.6 ÷ 10 = 25.06 </li></ul><ul><li>250.6 ÷ 100 = 2.506 </li></ul><ul><li>250.6 ÷ 10 = 0.02506 </li></ul><ul><li>250.6 ÷ 10 = 0.0002506 </li></ul>4 6
13. 13. Dividing by Powers of 10 <ul><li>Do some by yourself. </li></ul><ul><li>375 ÷ 10 = __________ </li></ul><ul><li>375 ÷ 10 = __________ </li></ul><ul><li>375 ÷ 100 = __________ </li></ul><ul><li>375 ÷ 10 = __________ </li></ul>0 4 9
14. 14. More difficult examples <ul><li>7.25 ÷ 1,000 = 0.00725 </li></ul><ul><li>0.036 ÷ 10 = 0.0036 </li></ul><ul><li>360,000 ÷ 10 = 3,600 </li></ul><ul><li>4,500 ÷ 10,000 = 0.45 </li></ul>2