Henry uses on average 99.8 gallons
of water per day. A gallon of water costs 0.9
pence. Henry is paying for the water he
used in the previous four weeks. Part a) Calculate an estimate for
the amount Henry pays.
We’ve been asked to find an
estimate for the amount Henry pays, which means we’re not looking for the exact
value, but just an approximation. We need to look at the numbers that
we’ve been given in the question and round them in such a way that it becomes easy
to work with them without a calculator.
A helpful rule of thumb to use when
approximating is that we should round each number to one significant figure. So 99.8 gallons is approximately
equal to 100 gallons when rounded to one significant figure. This is because the second
significant figure in this number is a nine. And as this is greater than five,
this tells us that we need to round up. So we round up the nine in the next
column. But it becomes 10. 99.8 is very close to 100. So this is going to be a sensible
approximation to use.
Now, 0.9 is actually already given
to one significant figure. But this number will be very easy
to work with. So we won’t use our rule of thumb
in this case. But instead, we’ll just round
sensibly. 0.9 is very close to one. So we can say that 0.9 pence is
approximately equal to one pence. 100 and one are going to be much
easier numbers to work with in our calculation than 99.8 and 0.9. And as they’re quite close to the
original values, they’ll give us a good approximation.
Now, let’s look at the calculation
that we’re going to use. We’re told that Henry is paying for
the water he used in the previous four weeks. This means that we’re working out
an estimate for the cost of the water used in the previous 28 days as there are
seven days in each week.
To work out our estimate of the
cost then, we need to multiply the number of days, which is 28, by the number of
gallons of water that Henry uses per day, which is approximately 100, and then by
the cost per gallon of water, which is approximately one pence.
Now, multiplying by one doesn’t
change a number. So in effect, all we’re doing is
multiplying 28 by 100. When we multiply a number by 100,
we move all of the digits two places to the left. So the two that was in the tens
column will now be in the thousands column. And the eight that was in the units
column will now be in the hundreds column. We can fill in the blank spaces
with zeros and it gives 2800.
So our estimate of the cost that
Henry pays is 2800 pence.
However, it would of course be far
more sensible to give our answer in pounds. So if you recall that one pound is
equal to 100 pence, then to convert our answer from pence into pounds, we need to
divide by 100. Dividing by 100 will just undo the
multiplication by 100 that we just did and leave us with an answer of 28.
Our estimate for the amount that
Henry pays for the previous four weeks is 28 pounds.
Part b) Is your estimate from the
previous part of the question an underestimate or an overestimate? Justify your answer.
To work out whether our answer is
an underestimate or an overestimate, we need to look whether the values we used in
calculating our estimate are bigger or smaller than the original values. Both 99.8 and 0.9 were rounded up
to give the values that we used in our calculation. As we then multiply these rounded
values together, this means that our estimate is bigger than the value we would’ve
got if we used the original values.
We can answer then that our
estimate is an overestimate as both the amount and the price of water were rounded
up and then multiplied.