The following equation is given 𝑎
equals 𝑏 multiplied by 𝑐. 𝑎 equals 2660.88 correct to two
decimal places. 𝑏 is equal to 760.2 correct to
four significant figures. Work out the lower bound for
Let’s start by rearranging the
given equation to make 𝑐 the subject. To make 𝑐 the subject, we need to
divide both sides of the equation by 𝑏. The equation for 𝑐 is, therefore,
𝑎 divided by 𝑏.
Since our equation for 𝑐 is in
terms of 𝑎 and 𝑏, we should next find the upper and lower bound of both 𝑎 and
𝑏. If 𝑎 is equal to 2660.88, then we
can find the lower and upper bounds by considering what 𝑎 might have been rounded
to if it had been rounded to the next number down and if it had been rounded to the
next number up.
If 𝑎 had been rounded to the
number below, that would give us 2660.87. If it had been rounded to the
number above though, that would give us 2660.89. We can find the lower bound by
finding the midpoint between 2660.87 and 2660.88, which is 2660.875. For the upper bound, we find the
midpoint of 2660.88 and 2660.89, which is 2660.885.
Remember, our value of 𝑎 will get
extremely close to 2660.885. However, it will never quite reach
it, since this number would actually round up to 2660.89. We can use inequality symbols to
show this. 𝑎 is greater than or equal to
2660.875 and less than 2660.885.
Let’s repeat this process for
𝑏. It’s been rounded to four
significant figures. If it had been rounded to the
number below, that would have been 760.1. And the number above is 760.3. To find the lower bound, we can
find the midpoint of 760.1 and 760.2, which is 760.15. The upper bound is the midpoint of
760.2 and 760.3, which is 760.25. Once again, we use the relevant
inequality symbols to show that the lowest possible value of 𝑏 is 760.15 but that
it’s also less than because it never quite reaches 760.25.
Now to find the lower bound for 𝑐,
we need to be a little bit careful. We want the lowest possible value
it could be. To achieve this, we need to divide
the smallest possible value of 𝑎 by the largest possible value of 𝑏. That’s the lower bound of 𝑎 and
the upper bound of 𝑏. The lower bound of 𝑐 is,
therefore, calculated by dividing 2660.875 by 760.25. That gives us that the lower bound
of 𝑐 is 3.5.