Question

11 Points Estimate the average by first rounding to the nearest 1,000: 1,000 2,300 2,600

Answer 1

Average = 2000

Explanation:

Given numbers are:

1,000 2,300 2,600

To find:

First round off the numbers to nearest 1000 and then find Average.

Solution:

1000 is already in thousands so no need to round off.

To round off a number to nearest thousand, we need check the digit on hundred's place.

• If the hundred's digit is greater than 5, we increase the thousand's digit by 1 and make the hundred's digit as 0.

• If the hundred's digit is lesser than 5, the thousand's digit remains the same and we make the hundred's digit as 0.

So, 2300 will be rounded off as 2000.

and 2600 will be rounded off as 3000.

Now, the numbers whose average is to be calculated are 1000, 2000, 3000.

Formula for average is given as:

`Average = \frac{\text{Sum of all numbers}}{\text{Count of numbers}}`

applying the formula:

`Average = (1000+2000+3000)/(3)\\\Rightarrow Average = (6000)/(3)\\\Rightarrow \bold{Average = 2000}`

So, the average after rounding off to nearest 1000 is 2000.