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# Estimate the following product using general rule: $578\times 161$

Last updated date: 23rd Mar 2023
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If the first non-zero digit from the left of a number is less than $5$, then the digit to its immediate left is left untouched and the digit used for reference is changed to zero. Similarly, if the first non-zero digit from the left of a number is greater than or equal to $5$, then the digit to its immediate left is increased by $1$ and the digit used for reference is changed to zero.
For example: Let’s consider the number $3251$ . Here, the first non-zero digit from the left is $1$. Since $1$ is smaller than $5$ , the digit to its immediate left, i.e. $5$ is left untouched and the reference digit, i.e. $1$ is changed to zero. So, the number, on rounding off, becomes $3250$ . Again, consider the number $3256$ . Here, the first non-zero digit from the left is $6$. Since $6$ is greater than $5$ , the digit to its immediate left, i.e. $5$ is increased by $1$ and the reference digit, i.e. $6$ is changed to zero. So, the number, on rounding off, becomes $3260$ .
Now, coming to the question, we are asked to estimate the value of $578\times 161$. The first number is $578$ . On rounding off to the nearest tens, we get $580$. We will further round it off to the nearest hundreds. So, on rounding off $580$ to nearest hundreds , we get $600$ . The second number is $161$ . On rounding off to the nearest tens, we get $160$. We will further round it off to the nearest hundreds. So, on rounding off $160$ to the nearest hundreds, we get $200$.
So, $578\times 161$ will be approximately equal to $600\times 200=120000$.
Hence, the estimated value of $578\times 161$ is $120000$.