Is there a typo in this? The calculation seems to give a result that is not accurate at all.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.
topsquark said:Is there a typo in this? The calculation seems to give a result that is not accurate at all.
\(\displaystyle \left ( \frac{4}{3} \right ) ^4 \approx 3.1605\)
You can take it from there.
-Dan
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").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.
An irrational number is a number that cannot be expressed as a fraction of two integers and has an infinite number of non-repeating decimals.
The value of irrational number π is approximately 3.14159265358979323846.
π is considered an irrational number because it cannot be expressed as a fraction of two integers and its decimal representation never terminates or repeats.
The value of π was first calculated by Archimedes in the 3rd century BC using a geometric method. Since then, various mathematicians have used different methods to calculate π with increasing precision.
π is a fundamental constant in mathematics and is used in many mathematical formulas and equations, particularly in geometry and trigonometry. It also has applications in fields such as physics, engineering, and statistics.