Question

Estimate the product $475\times 225$ rounding off each number to the nearest hundred.

Answer 1

Hint: In the question we have to estimate the product $475\times 225$ by rounding off each number to the nearest hundred for this first we will understand what does rounding off means then we will learn how we can round off a number nearest to tens and nearest to hundred then we will use this in our question to get out required answer.

Complete step-by-step solution:
Rounding off means we are making the number simpler by keeping its value intact but closer to the next number.
Rounding off of a number is done nearest to tens, nearest to hundreds, nearest to thousands, and so on.
For rounding off the number to the nearest tens we will observe digits at unit place.
If the digit at unit place is greater than or equal to $5$. Then we will add $1$ to the place and the unit place will become $0$.
If the digit at tens place is less $5$. Then the digit at the unit place will become $0$.
 For rounding off the number to the nearest hundred we will observe digits at tens place.
If the digit at tens place is greater than or equal to $5$. Then we will add $1$ to hundreds of places and tens of places and unit place will become $0$.
If the digit at tens place is less $5$. Then the digit at tens place and unit place will become $0$.
Now let us proceed to our question
In the question we have to estimate the product of $475\times 225$ to the nearest hundred
Now we will round off each term
First we will round off $475$ nearest to hundred.
We can see digit at tens place if $7$ which is greater than $5$ so we will add $1$ to digit at hundreds place and digit at tens place and unit place will become $0$
After rounding off $475$ nearest hundred $475$ becomes $500$ .
Now we will round off $225$ nearest hundred.
We can see digit at tens place if $2$ which is lesser than $5$ so we will make digit at tens place and unit place will become $0$
After rounding off $225$ nearest hundred $225$ become $200$.
Now we will multiply both rounded off terms
$500\times 200$
$\Rightarrow 100000$
$\therefore 100000$ is our required answer.
Hence the estimated product of $475\times 225$ rounding off each number to the nearest hundred is $100000$.

Note: Rounding off is mainly used to make the value simpler. It will give us an estimated value. If we want to round off a number nearest to thousand we will observe a digit at hundreds place , similarly if we want to round off a number nearest to ten thousand we will observe digit at thousands place and so on.