Hey there! Sign in to join this conversationNew here? Join for free

Need help with significant figures in basic uncertainty calculation watch

    • Thread Starter
    Offline

    0
    ReputationRep:
    The following is from a book:

    The fractional uncertainty of a product or quotient of 2 quantities is the sum of the fractional uncertainties of those 2 quantities, i.e.

    r = xy or r = x/y
    dr/r = dx/x + dy/y

    e.g. Two lengths are reported as: x = 18.5 +/- 0.5 mm, y = 12.5 +/- 0.5 mm

    dr/r = 0.5/18.5 + 0.5/12.5 = 0.067
    r = 18.5 x 12.5 = 231.25
    dr = 0.067 x 231.25 = 15.49 = 20 mm (1 sf)

    r = 230 +/- 20 mm

    (the underlines are mine)

    I'm confused as to how the rounding ups come about.
    How did 231.25 become 230? Where does the 2 sf come from? Why not 3 sf and 231 since it's multiplication and the quantity with the lowest sf has 3 sf?
    Shouldn't dr/r be 0.07? 0.5/18.5 = 0.03 (1 sf, following number of sf in 0.5 for division), 0.5/12.5 = 0.04, 0.03 + 0.04 = 0.07
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.