Question

Find a low and high estimate for the product or quotient. (p. 748)

$371\times 47$.

Short answer

The low estimate is12000, and the high estimate is20000.

Step-by-step solution

Step-1 – Concept of low and high estimate of product

To find the low estimate, replace all the digits after leading digit with zeros.

To find the high estimate, increase the leading digit by 1 and replace all the digits after the first with zeros.

Step-2 – Find the low estimate

To find the low estimate, replace all the digits after leading digit with zeros.

So, the low estimate of the product is

$\begin{array}{l}\underset{¯}{\begin{array}{l}300\\ \times 40\end{array}}\\ 12000\end{array}$

Thus, the low estimate of the product is 42000.

Step-3 – Find the high estimate

To find the high estimate, increase the leading digit by 1 and replace all the digits after the first with zeros.

So, the high estimate of the product is

$\begin{array}{l}\underset{¯}{\begin{array}{l}400\\ \times 50\end{array}}\\ 20000\end{array}$

Thus, the high estimate of the product is 50000.