How precise is (4/3)^4 compared to π?

In summary, the value of π is 3.1415926535 and when using a calculator, the quantity (4/3)^4 agrees with π to one decimal place.
  • #1
mathdad
1,283
1
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
  • #2
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.

\(\displaystyle \left ( \frac{4}{3} \right ) ^4 \approx 3.1605\)

You can take it from there.

-Dan
 
  • #3
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

Ok. I will check the textbook. However, I am sure there is no typo. I will come back later tonight.
 
  • #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.
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").
 
  • #5
Thank you everyone.
 

Related to How precise is (4/3)^4 compared to π?

What is an irrational number?

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.

What is the value of irrational number π?

The value of irrational number π is approximately 3.14159265358979323846.

Why is π considered an irrational number?

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.

How was the value of π calculated?

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.

What is the significance of π in mathematics?

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.

Similar threads

  • General Math
Replies
4
Views
1K
  • General Math
Replies
4
Views
1K
Replies
4
Views
656
Replies
8
Views
1K
  • General Math
Replies
5
Views
3K
  • General Math
Replies
1
Views
1K
Replies
12
Views
2K
Replies
9
Views
2K
Replies
4
Views
2K
Replies
1
Views
1K
Back
Top