Asked by Prethy
determine the number of digits in the expansion (2^120)(5^125) without using a calculator or computer
Find the coordinates of the two points that trisect the line segment with endpoints A(2,3) and B (8,2)
Find the coordinates of the two points that trisect the line segment with endpoints A(2,3) and B (8,2)
Answers
Answered by
MathMate
(2^120)(5^125)
=(2*5)^120 * 5^5
=10^120 * 3125
Therefore there are 124 digits.
Note:
To multiply by 5, you can multiply by 10 and divide by 2.
5^2=25
5^3=125
5^4=625
5^5=3125
Let the two points be H and K, such that AHKB is a straight line.
H=(Xa+(Xb-Xa)/3,Ya+(Yb-Ya)/3)
K=(Xa+2(Xb-Xa)/3,Ya+2(Yb-Ya)/3)
=(2*5)^120 * 5^5
=10^120 * 3125
Therefore there are 124 digits.
Note:
To multiply by 5, you can multiply by 10 and divide by 2.
5^2=25
5^3=125
5^4=625
5^5=3125
Let the two points be H and K, such that AHKB is a straight line.
H=(Xa+(Xb-Xa)/3,Ya+(Yb-Ya)/3)
K=(Xa+2(Xb-Xa)/3,Ya+2(Yb-Ya)/3)
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