Question

What is the estimated value of \[786\times 1385\]?

Answer 1

Hint: Estimation uses round numbers in a calculation to make it quicker or easier to get an approximate answer. We will first round off the given numbers, such that its calculation becomes easy and accuracy is maintained to some extent. Then multiply those rounded off numbers to find the estimated product of the given numbers.

Complete step by step answer:
 To estimate a number, we first round off the number using general rule, which is, we look at the digit to the right of the digit that we want to round off, if it is less than \[5\], then value of digit is not changed, if the digit to the right is \[5\] or more than \[5\], then the value of digit which we are rounding off get replaced by its successor.
Now, to estimate the product of the numbers, the general rule is that we round it off to that number of digits that seems to give a more accurate result with easier calculation.
For e.g., if we want to round off \[6612\] to find its product with a number which is already rounded off to \[2000\], then we can round off \[6612\] to \[6610\] (rounded off to nearest ten), which won’t help as calculation is still long. Also, we can round it off to \[7000\] (rounded off to nearest thousand), where calculation is easy but the answer will be less accurate. So, a better way to do this is that we round it off to \[6500\], so accuracy will be maintained and calculation will also be easy.
Now, to find the estimated product of the given question, we start with rounding of our numbers, that is \[786\]and \[1385\].
We will round off \[786\] to the nearest hundred, so we get \[800\].
We will round off \[1385\] to the nearest hundred, so we get \[1400\].
To find estimated product, we multiply this rounded off numbers, as follows:
\[\begin{align}
& \Rightarrow 786\times 1385 \\
& \Rightarrow 800\times 1400 \\
& \Rightarrow 8\times 100\times 14\times 100 \\
& \Rightarrow 8\times 14\times 100\times 100 \\
\end{align}\]
\[\begin{align}
& \Rightarrow 112\times 10000 \\
& \Rightarrow 1120000 \\
\end{align}\]
Hence, the estimated product of \[786\] and \[1385\] is $1120000$.

Note:
It’s not important to round off all numbers to the same value. Estimate each number individually taking in consideration the easy calculation and closest number.This method only gives us an estimate of the product of two numbers, that is, to which value the product will be near to. This is not the exact value or approximate value and hence should not be used where exact or approximate values are required.