MHB How precise is (4/3)^4 compared to π?

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The discussion focuses on comparing the value of (4/3)^4 with π, which is approximately 3.1415926535. The calculated value of (4/3)^4 is about 3.1605, leading to confusion about its accuracy. It is clarified that (4/3)^4 equals 3.1604938271604938271604938271605, which agrees with π to one decimal place. The discrepancy arises because the second decimal place differs, indicating a lack of precision in the comparison. The conversation emphasizes the importance of accurate calculations in mathematical comparisons.
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The value of the irrational number π, correct to ten decimal places (without rounding) is 3.1415926535. By using your calculator, determine to how many decimal places does the quantity (4/3)^4 agree with π.
 
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RTCNTC said:
The value of the irrational number π, correct to ten decimal places (without rounding) is 3.1415926535. By using your calculator, determine to how many decimal places does the quantity (4/3)^4 agree with π.
Is there a typo in this? The calculation seems to give a result that is not accurate at all.

[math]\left ( \frac{4}{3} \right ) ^4 \approx 3.1605[/math]

You can take it from there.

-Dan
 
topsquark said:
Is there a typo in this? The calculation seems to give a result that is not accurate at all.

[math]\left ( \frac{4}{3} \right ) ^4 \approx 3.1605[/math]

You can take it from there.

-Dan

Ok. I will check the textbook. However, I am sure there is no typo. I will come back later tonight.
 
RTCNTC said:
The value of the irrational number π, correct to ten decimal places (without rounding) is 3.1415926535. By using your calculator, determine to how many decimal places does the quantity (4/3)^4 agree with π.
Couldn't you have just done this? Using a calculator, as the problem says, (4/3)^4= 3.1604938271604938271604938271605. That "agrees with π" to one decimal place ("3.1") since it differs in the second decimal place ("6" instead of "4").
 
Thank you everyone.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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