(a) A 3 % uncertainty means a 3% uncertainty on the measured value.
The measured value is [tex] v=70 km/h [/tex]. The 3 % of this value is
[tex] v \cdot \frac{3}{100}=(70 km/h)\frac{3}{100}=2.1 km/h [/tex]
So, the highest and lowest values are:
[tex] v_H = 70 km/h + 3\%=70 m/h+2.1 km/h=72.1 km/h [/tex]
[tex] v_L =70 km/h-3 \%=70 km/h-2.1 km/h=67.9 km/h [/tex]
(b) To find the highest and lowest speeds in mi/h, we need to convert [tex] v_H, v_L [/tex] into these units. keeping in mind that
[tex] 1 mi = 1.609 km [/tex]
we have:
[tex] v_H=72.1 \frac{km}{h} \cdot \frac{1}{1.609 km/mi} =44.8 mi/h [/tex]
[tex] v_L=67.9 \frac{km}{h} \cdot \frac{1}{1.609 km/mi}=42.2 mi/h [/tex]
