Value of Irrational Number π (Part 1)

[mathdad]

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?

 

[Evgeny.Makarov]

Where do you need help with this problem?

 

[mathdad]

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?

 

[Evgeny.Makarov]

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.

Can we show that (4/3)^4 in terms of decimal places agrees with pi?

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

 

[mathdad]

Then this should be said in the original question to not make people guess.

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

The original question has been edited.