Estimate the product 1391 x 492 by rounding off each number to its nearest hundreds. Please answer. I will follow you.
The Correct Answer and Explanation is:
To estimate the product of 1391×4921391 \times 4921391×492 by rounding each number to the nearest hundred:
- Round 1391 to the nearest hundred:
The hundreds digit is 3 (since 1391 is between 1300 and 1400). Since 1391 is closer to 1400 than to 1300, we round it up to 1400. - Round 492 to the nearest hundred:
The hundreds digit is 4 (since 492 is between 400 and 500). Since 492 is closer to 500 than to 400, we round it up to 500.
Now, multiply the rounded numbers:1400×500=700,0001400 \times 500 = 700,0001400×500=700,000
Explanation:
Rounding numbers makes calculations easier and quicker, especially when you only need an approximation. Here’s why the steps above are reasonable:
- Rounding: Numbers are rounded to the nearest hundred to simplify the computation. This helps in estimating the product without going into the exact multiplication of the original numbers.
- Approximation: Since we rounded both 1391 and 492 to 1400 and 500, respectively, the result is an estimate, not an exact value. The actual product would be a bit less than this because the rounded values are slightly higher than the original numbers.
Finally, after rounding and multiplying, we get the estimated product of 700,000.
The actual product of 1391 and 492 is 684,132. As we can see, the estimate of 700,000 is close to the real answer, which is a great example of how rounding can be a useful tool for fast calculations when precision is not crucial.
