How to do significant figures?
HELP ME PLEASE WITH A HOMEWORK QUESTION. Martin won the 400 metre race in school sports day with a time of 1 minute. The distance was correct to the nearest 10 centimetres. The time was correct to the nearest tenth of a second. (A) work out the upper boulevard the lower bound of Martin's speed in km/h. Give your answers correct to five significant figures. (B)Write down an appropriate value for Martin's speed in km/h. Explain your answer.
Comments
10 centimetres is 1/10 of a metre
=> 399.95 ≤ d < 400.05 (metres)
=> 59.95 ≤ t < 60.05 (seconds)
Speed is d/t, so upper bound is 400.05/59.95 = 6.6731 m/s
=> lower bound is 399.95/60.05 = 6.6603 m/s
So, in km/h --> upper bound is (6.6731 x 60)/1000 km/min
i.e. 0.40038 x 60 km/h ---> 24.023 km/h
--> lower bound is (6.6603 x 60)/1000 km/min
i.e. 0.39962 x 60 km/h ---> 23.977 km/h
An appropriate value would be central to this.
i.e. 24 km/h
400m/1.0min * [km/100m] * [60min/hr]
= (400*60)km/ 100hr = 240km/hr
Now for 5 significant figures we get 240.00 km/hr
By the way, nearest cm is 40000. For five figures.
In seconds, 60. Is good to only 2 significant figures.
Technically, the answer can only have the same amount of figures as the element with the least amount of significant digits.