MHB Value of Irrational Number π (Part 1)

AI Thread Summary
The value of the irrational number π is approximately 3.1415926535, accurate to ten decimal places. The discussion revolves around determining how closely the quantity (4/3)^4, which is derived from the Rhind papyrus, approximates π. Participants explore whether this calculation can be performed without a calculator, suggesting the use of long division to compute (4/3)^4 as 256/81. The conversation emphasizes the need for clarity in the original question to avoid confusion. Ultimately, the goal is to establish the decimal agreement between (4/3)^4 and π.
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The value of irrational number π, correct to ten decimal places (without rounding), is 3.1415926535. By using your calculator, determine to how many decimal places the following quantity [(4/3)^4] agrees with π.

The value used for π in the Rhind papyrus, an ancient Babylonian text written about 1650 B.C. is (4/3)^4.

I was wondering if this question can be answered without a calculator. Can we show that (4/3)^4 in terms of decimal places agrees with pi?
 
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Where do you need help with this problem?
 
Evgeny.Makarov said:
Where do you need help with this problem?

I was wondering if this question can be answered without a calculator. Can we show that (4/3)^4 in terms of decimal places agrees with pi?
 
RTCNTC said:
I was wondering if this question can be answered without a calculator.
Then this should be said in the original question to not make people guess.

RTCNTC said:
Can we show that (4/3)^4 in terms of decimal places agrees with pi?
You can use long division to compute $$\left(\frac43\right)^4=\frac{256}{81}$$ to a few decimal places.
 
Evgeny.Makarov said:
Then this should be said in the original question to not make people guess.

You can use long division to compute $$\left(\frac43\right)^4=\frac{256}{81}$$ to a few decimal places.

The original question has been edited.
 
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