Timmy loves converting numbers from Fahrenheit to Celsius. Timmy also loves getting carried away.
One day, Timmy converted the temperature from Fahrenheit to Celsius. Pretending that the number he obtained was
a temperature in degrees Fahrenheit, he then converted it to Celsius. He repeated this process indefinitely. He noticed that his values were getting closer and closer to a
number. What number?
Repeatedly going through the process of
a) subtracting 32
b) multiplying by 5/9
will eventually approach -40, the temperature at which the Farenheit reading is the same as the Celsius reading.
For example, starting with 500:
500
260
126.6666666666667
52.5925925925926
11.440329218107
-11.4220393232739
-24.12335517959661
-31.17964176644256
-35.09980098135698
-37.277667211865
-38.48759289548055
-39.15977383082252
-39.5332076837903
-39.74067093543906
-39.85592829746614
-39.91996016525896
-39.95553342514388
-39.97529634730215
-39.9862757485012
-39.992375415834
-39.99576411990777
-39.9976467332821
-39.99869262960116
-39.99927368311175
-39.99959649061763
-39.9997758281209
-39.99987546006717
-39.99993081114842
-39.99996156174913
-39.9999786454162
-39.99998813634232
-39.99999340907907
-39.99999633837726
-39.99999796576515
-39.99999886986953
-39.99999937214974
-39.99999965119431
-39.99999980621907
-39.99999989234393
this being a successive approximations solution of x = (x - 32) * 5/9
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Posted by Charlie
on 2019-07-23 13:06:16 |
solution
