What is Pi? explain.
2 answers:
Pi (pronounced like "pie") is often written using the symbol π
Circumference divided by the Diameter of a Circle. π = 3.14
The circumference divided by the diameter of a circle is always π, no matter how large or small the circle is!
We can use π to find a Circumference when we know the Diameter
Using Pi
Circumference = π × Diameter
Example: You walk around a circle which has a diameter of 100 m, how far have you walked?
Distance walked = Circumference
= π × 100 m
= 314.159... m
= 314 m (to the nearest m)
Also we can use π to find a Diameter when we know the Circumference
Diameter = Circumference / π
Example: Sam measured 94 mm around the outside of a pipe ... what is its Diameter?
Diameter = Circumference / π
= 94 mm / π
= 29.92... mm
= 30 mm (to the nearest mm)
Radius
The radius is half of the diameter, so we can also say:
For a circle with a radius of 1
The distance half way around the circle is π = 3.14159265...
Digits
π is approximately equal to:
3.14159265358979323846…
The digits go on and on with no pattern.
π has been calculated to fifty trillion decimal places and still there is no pattern to the digits
Approximation
A quick and easy approximation for π is 22/7
22/7 = 3.1428571...
But as you can see, 22/7 is not exactly right. In fact π is not equal to the ratio of any two numbers, which makes it an irrational number.
A really good approximation, better than 1 part in 10 million, is:
355/113 = 3.1415929...
(think "113355", slash the middle "113/355", then flip "355/113")
Summary:
22/7 = 3.1428571...
355/113 = 3.1415929...
π = 3.14159265..
Remembering The Digits
You usually just remember "3.14159", but you can also count the letters of:
"May I have a large container of butter today"
3 1 4 1 5 9 2 6 5
Circumference divided by the Diameter of a Circle. π = 3.14
The circumference divided by the diameter of a circle is always π, no matter how large or small the circle is!
We can use π to find a Circumference when we know the Diameter
Using Pi
Circumference = π × Diameter
Example: You walk around a circle which has a diameter of 100 m, how far have you walked?
Distance walked = Circumference
= π × 100 m
= 314.159... m
= 314 m (to the nearest m)
Also we can use π to find a Diameter when we know the Circumference
Diameter = Circumference / π
Example: Sam measured 94 mm around the outside of a pipe ... what is its Diameter?
Diameter = Circumference / π
= 94 mm / π
= 29.92... mm
= 30 mm (to the nearest mm)
Radius
The radius is half of the diameter, so we can also say:
For a circle with a radius of 1
The distance half way around the circle is π = 3.14159265...
Digits
π is approximately equal to:
3.14159265358979323846…
The digits go on and on with no pattern.
π has been calculated to fifty trillion decimal places and still there is no pattern to the digits
Approximation
A quick and easy approximation for π is 22/7
22/7 = 3.1428571...
But as you can see, 22/7 is not exactly right. In fact π is not equal to the ratio of any two numbers, which makes it an irrational number.
A really good approximation, better than 1 part in 10 million, is:
355/113 = 3.1415929...
(think "113355", slash the middle "113/355", then flip "355/113")
Summary:
22/7 = 3.1428571...
355/113 = 3.1415929...
π = 3.14159265..
Remembering The Digits
You usually just remember "3.14159", but you can also count the letters of:
"May I have a large container of butter today"
3 1 4 1 5 9 2 6 5
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