Question

17.

Peter transports metal bars in his van.
The van has a safety notice: "Maximum Load 1200 kg".
Each metal bar has a label: "Weight 60 kg".
For safety reasons, Peter assumes that:
1200 is rounded correct to 2 significant figures, and
60 is rounded correct to 1 significant figure.
Calculate the greatest number of bars that Peter can safely put into the van if his assumptions are
correct.

Answer 1

17 bars

Explanation:

Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.

Range of values

The error in a rounded number is assumed to be as much as half of the least significant digit of the number.

Peter's load limit may actually be as low as ...

1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100

Peter's bar weight might be as high as ...

60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10

Safe loading

If Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...

(1150 kg) / (65 kg/bar) ≈ 17.7 bars

The greatest number of bars Peter can load safely is 17.