Get an answer in 5 minutes

We'll notify as soon as your question has been answered.

Plus iconAsk a question to our educators
MATHS
Asked by Omar

Helen draws a random circle. she then measure it diameter and circumference. should get a circumference, C, of 405mm correct to 3 significant figures she get a diameter, D, of 130mm correct 2 significant figures. Helen want to find the value of Pi using a formula Pi =D/C calculate the lower bound and upper bound for Helen's value of pi give your answer correct to 3 decimal place?

First, you want to find the lower and upper bounds of the circumference C and diameter D. C = 405mm to 3sf so the bounds are: 404.5 to 405.5 We find this by subtracting/adding half the degree of accuracy. Here it is 1mm, looking at 3rd significant figure. D = 130mm to 2sf so the bounds are: 125 to 135 Here the degree of accuracy is 10mm, looking at the 2nd significant figure. Now you consider the combination of figures which will give you the lowest and highest possible value for pi, as given by pi = C/D To get the lowest value we can see that we need to combine the smallest possible C with the highest possible D LB: 404.5/135 = 2.996 (3dp) For the highest value we need the reverse UB: 405.5/125 = 3.224 (3dp) Notice how the true value of pi falls within these bounds.

Megha's profile picture
Verified
Megha Sanjeev
·

3.1k students helped

If we’re looking for the lowerbound of pi, the circumference C would have to be at its smallest and the diameter D would have to be at its highest. For the upper bound it would be the other way around. So for the lower bound: 405mm (3 s.f.) => 404.5 (lowest possible) 130mm (2 s.f.) => 134.499... (highest possible) lower bound pi = 3.007 (3d.p) So for the higher bound: 405mm (3 s.f.) => 405.4999… (highest possible) 130mm (2 s.f.) => 125.0 (lowest possible) upper bound pi = 3.244 (3d.p)

Mujavid's profile picture
Verified
Mujavid Bukhari
·

6.2k students helped

Similar Maths questions

Maths

Asked by Tink

4-x<9

Get an answer in 5 minutes

We'll notify as soon as your question has been answered.

Plus iconAsk a question to our educators

Badge showing the text 'New'Learn Maths with Video Lessons

GCSE Maths - Numbers
1hr 28m · 8 videos
Paja's profile picture
Paja Kruzikova
·

442 students helped

GCSE Maths - Numbers
Quadratic Inequalities
28m · 3 videos
Iqbal's profile picture
Iqbal Lokman
·

1.3k students helped

Quadratic Inequalities
GCSE Maths - Ratios
1hr 32m · 9 videos
Paja's profile picture
Paja Kruzikova
·

442 students helped

GCSE Maths - Ratios
GCSE Maths - Algebra A
56m · 6 videos
Paja's profile picture
Paja Kruzikova
·

442 students helped

GCSE Maths - Algebra A

Premium video lessons available now on Scoodle

50% discount available

Scoodle's video lessons make learning easy and fun. Try it for yourself, the first lesson is free!