How does the ratio change when the number of drops increases?
A
a
Example Solution:
Number of Drops
Number of Hits
25
15
50
31
100
63
B
b
Example Solution:
Number of Drops
Ratio
25
≈ 3.33
50
≈ 3.23
100
≈ 3.17
C
c
The ratio is closer to π when the number of drops increase.
Practice makes perfect
a
We are given the instructions and asked to perform an experiment with a needle or toothpick. We will drop the needle onto the paper and see if it touches one of the drawn lines. This will be our hit. Let's record the number of hits after 25, 50, and 100 drops.
Number of Drops
Number of Hits
25
15
50
31
100
63
b
In this part we are asked to evaluate the ratio of two times the total number of drops to the number of hits after 25, 50, and 100 drops. To do this let's use the table from the previous part.
Number of Drops
Number of Hits
Ratio
25
15
2( 25)/15≈ 3.33
50
31
2( 50)/31≈ 3.23
100
63
2( 100)/63≈ 3.17
c
Let's recall that π≈ 3.14. Looking at the table we made in Part B, we can see that the ratio is closer to π when the number of drops increases.
