How precise is (4/3)^4 compared to π?

[mathdad]

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.

 

[topsquark]

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

 

[mathdad]

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.

 

[HOI]

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").

 

[mathdad]

Thank you everyone.