Question

How do you estimate $1087\times 21$ by rounding?

Answer 1

Hint: In this question we will try to estimate the value of the product by rounding the digits such that we can calculate the product mentally. We will look at the different cases by rounding up the number to the value of the nearest tens, nearest hundredth and the nearest thousand. We will also compare the estimate value with the actual value of the number.

Complete step by step solution:
We have the expression given to us as:
$\Rightarrow 1087\times 21$
Now on rounding both the numbers to the nearest tens place, we get:
$\Rightarrow 1087\to 1090$
$\Rightarrow 21\to 20$
Therefore, we can write it as:
$\Rightarrow 1087\times 21\approx 1090\times 20$
On simplifying, we get:
$\Rightarrow \approx 21800$
Now on rounding both the numbers to the nearest hundredths place, we get:
$\Rightarrow 1087\to 1100$
Notice that $21$ will be still in the nearest tens place since it has only two digits.
$\Rightarrow 21\to 20$
Therefore, we can write it as:
$\Rightarrow 1087\times 21\approx 1100\times 20$
On simplifying, we get:
$\Rightarrow \approx 22000$
Now on rounding both the numbers to the nearest thousandths place, we get:
$\Rightarrow 1087\to 1100$
Notice that $21$ will be still in the nearest tens place since it has only two digits.
$\Rightarrow 21\to 20$
Therefore, we can write it as:
$\Rightarrow 1087\times 21\approx 1000\times 20$
On simplifying, we get:
$\approx 20000$.
Now the actual value of $1087\times 21=22827$.
We can see that the closest estimated value to the actual value is the first one. The numbers which are rounded to tens place followed by the hundredths place and then finally the thousandths place. Therefore, the degree of rounding affects the error of the estimated value.

Note:
It is to be remembered that rounding is done to make the number to the nearest multiple of tens place. It is to be remembered that when the number is followed by the numbers $5,6,7,8,9$ the number is to be rounded upwards to the nearest multiple of ten and if it is followed by $0,1,2,3,4$ then it is to be rounded downwards to the nearest multiple of ten.