Daisy and Harry have used different methods to show that the estimate on the whiteboard is an underestimate.
a) Who has the faster method? Write a sentence to explain your answer.
b) Harry's method will work on any calculation. Give an example of a calculation where Daisy's method doesn't work.
Q Both numbers have been rounded down so this must be an underestimate.
If both numbers had been rounded up, it would be an overestimate.
I worked out the calculation and the actual answer is $30,679.3$ so the estimate is an underestimate.
\[
\begin{aligned}
127.3 \times 241 & \approx 100 \times 200 \\
100 \times 200 & =20,000
\end{aligned}
\]
Answer
\(\boxed{\text{b) Example: } 100 * 250.5 \text{, where Daisy's method results in an overestimate.}}\)
Step 1 ：Daisy's method: Round down both numbers: \(100 * 200 = 20,000\)
Step 2 ：Harry's method: Round up both numbers: \(128 * 242 = 30,848\)
Step 3 ：Neither method is faster than the other, as both methods involve the same number of steps.
Step 4 ：Daisy's method doesn't work when one or both of the numbers cannot be rounded down, such as when one of the numbers is already a whole number. An example is \(100 * 250.5\), where Daisy's method results in an overestimate instead of an underestimate.
Step 5 ：\(\boxed{\text{a) Neither method is faster than the other.}}\)
Step 6 ：\(\boxed{\text{b) Example: } 100 * 250.5 \text{, where Daisy's method results in an overestimate.}}\)
