Question

Estimation Estimate the sum or difference by rounding each number to the place of its leading digit. (p. 747)

$112+193+583$.

Short answer

The sum is about900.

Step-by-step solution

Step-1 – Concept of leading digit

The leading digit is the first digit in any number. Rounding to the place of leading digit means rounding off the number to the nearest place value of the leading digit.

For example, in the number 2345 the leading digit is in thousand place, so we round it to the nearest thousand. Since the digit next to leading digit is less than 5, so it will get rounded to 2000.

Step-2 – Rounding of the numbers

In the given sum, observe that each number has three digits.

So, the leading digit is in the hundredth place. So, we’ll round each number to the nearest hundred and then estimate the sum.

Step-3 – Estimate the sum

To estimate the sum, round each number to nearest hundredth and then add them to get

$\begin{array}{l}112+193+583\approx 100+200+600\\ =300+600\\ =900\end{array}$

Thus, the sum is about 900.