# math 115

How many droplets of water are in a river that is 100 km long, 290 m wide, and 29 m deep? Assume a droplet is 1 milliliter. (Note: one liter equals one cubic decimeter and 10 decimeters equals 1 meter.)

Express you answer in scientific notation.

841000000(1000000)=8.41^14/8.41^13

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1. volume=width*hight*lenght
volume=100, 100m*290*29m
volume=29000029m^3
icubic meter=1000,000meter
then there is 29000029
cubic meter
2.9000029*10^13

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2. 1 m = 10 dm

1 km = 1,000 m = 10,000 dm

100 km * 290 m * 29 m =

100 * 10,000 dm * 290 * 10 dm * 29 * 10 dm =

( 1,000,000 * 2,900 * 290 ) dm ^ 3 =

( 10 ^ 6 * 2.9 * 10 ^ 3 * 2.9 * 10 ^ 2 ) dm ^ 3 =

( 10 ^ 6 * 10 ^ 3 * 10 ^ 2 ) * ( 2.9 * 2.9 ) dm ^ 3 =

( 10 ^ 11 * 2.9 ^ 2 ) dm ^ 3

( 10 ^ 11 * 8.41 ) dm ^ 3 =

8.41 * 10 ^ 11 dm ^ 3 = 8.41 * 10 ^ 11 liters

1 liter = 1,000 ml = 10 ^ 3 ml = 10 ^ 3 droplets

8.41 * 10 ^ 11 * 10 ^ 3 = 8.41 * 10 ^ 14 droplets

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3. volume = (100)(290)(29) km^3
= 841000 km^3
= 8.41 x 10^5 km^3

1 km = 1000 m
1 km^3 = (1000m)^3 = 10^9 m^3
1 m = 1000 mm
1 m^3 = (1000 mm)^3 = 10^9 mm^3

then 1 km^3 = (8.41 x 10^5)(10^9)(10^9) mm^3
= 8.41 x 10^23 mm^3

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4. Reiny

Volume isn't (100)(290)(29) km^3

a river is 100 kilometers long

290 meters wide

and 29 meters deep

1 km = 1000 m

1 m = 1 / 1000 m

290 m = 290 / 1000 = 0.29 km

29 m = 29 / 1000 = 0.029 km

Volume = ( 100 * 0.29 * 0.029 ) km ^ 3 = 0.841 km ^ 3 = 8.41 * 10 ^ - 1 km ^ 3

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5. Bosnian, you are correct, I should look at the units more carefully
Volume= (100)(.290)(.029) km^3
= .841 km^2

etc

thanks for catching my error, the answers seemed unreasonably hight.

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