A cafe sold exactly 1100 hot drinks in a week.
The owner says that 40% of these hot drinks were coffees. This percentage is correct to 1 s.f.
a) What is the smallest the percentage could actually have been?
b) What is the smallest number of coffees the cafe could actually have sold in this week?
a) The smallest percentage that is rounded to 40% when rounded to 1 significant figure is 35%. To see why, we can consider the possible ranges of numbers that round to 40%. Any number from 40.0 to 44.9% will round to 40% when rounded to 1 s.f. However, if the actual percentage were 39.9% or lower, it would round down to 30%. The only range that includes 35% is 35.0 to 39.9%, so the smallest percentage that rounds to 40% is 35%.
b) If 40% of the hot drinks were coffees, then we can find the number of coffees by multiplying 1100 by 0.4:
1100 x 0.4 = 440
So the cafe sold at least 440 coffees in this week. However, this may not be the smallest possible number. To see why, let's consider the possible ranges of numbers that round to 40% (as we did in part a). Any number from 40.0 to 44.9% will round to 40% when rounded to 1 s.f. If the actual percentage were 39.9% or lower, it would round down to 30%.
Let's calculate how many coffees the cafe would have sold if the percentage were 39.9%:
1100 x 0.399 = 439.9
This rounds down to 440 when rounded to 1 s.f., which means that the smallest possible number of coffees the cafe could have sold is 440.
To find the answers to these questions, we need to calculate the range of possible values based on the given information.
a) To find the smallest possible percentage, we need to calculate 40% of 1100 and then round it to 1 significant figure.
40% of 1100 = 0.4 * 1100 = 440
Rounded to 1 significant figure, the smallest possible percentage is 400.
b) To find the smallest number of coffees sold, we need to calculate 40% of the total number of hot drinks.
40% of 1100 = 0.4 * 1100 = 440
Therefore, the smallest number of coffees the cafe could have sold in this week is 440.