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.
mathdad
Messages
1,280
Reaction score
0
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.
 
Mathematics news on Phys.org
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.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Back
Top