Estimation Using Powers of 10

Estimation Using Powers of 10

• Question:  How many basketballs fit in a gym?

Background Information:

100			one
101			ten
102			one hundred
103			one thousand
104			ten thousand
105			one hundred thousand
106			one million
107			ten million
108			one hundred million
109			one billion
1010			ten billion

     From this information above, the powers are equal to the written number on the left of it.  However, how do we decipher if a power should be rounded up a power or rounded down?

     The class knows 10 to the 1/2 power is approximately 3.16.  10 to the  2.5 power is estimated to 316.  The decimal point keeps moving to the left.  If the measurement is more than 3.16, then round up.  If it is shorter or equal to, round down.  It is logic if the volume of something, like a gym, length is closer to 10 to the power of 0 or 10 to the power of 1.  

     Lab:

    A discussion with the class decided that the length, width, and heighth would each be 10 to the first power because it makes more sense. Looking at the table above, one meter is way too small, and 100 meters would be the size of a football field, or a very large gym, that any school in the district, possibly in the state, does not have.  

1.    Cube Formula: Then, take the length, width, and height and multiply them together to get 10 to the third.  Divide by the estimated volume of a basketball, 10 to the third.  This was calculated pretending the basketball was in a box, leaving a little room that would be in between each basketball. This will equal 10 to the sixth, or approximately one million basketballs!!
2.    Sphere Formula:  Another example is multiplying 4 times 10 to the negative 3, disregarding the extra room to be more exact with the basketball itself.  This equals 10 to the negative 2 power.  Divide the volume, still the same, 10 to the third, and 10 to the negative 2, and get 10 to the fifth.  Now, this is where the half measurements of powers needs to be used.  10 to the sixth is closer to 316,000, rather then 10 to the fifth, 100,000.  The same conclusion was drawn: estimated one million basketballs would fit!

Yes, more websites!

http://www.isthe.com/chongo/tech/math/number/tenpower.html  (This ones boring!)

http://www.mathsisfun.com/index-notation-powers.html