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

AI Thread Summary
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.
 

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