5th Grade estimation problem.

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Helpmewithmymath

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There are two estimation problems. I need to know why the 4 digit numbers in each of these problems are rounded differently.
1. A rectangular wall measures 1,620 cm by 68 cm. Estimate the area of the wall. The textbook calculation shows that 1,620 is rounded to 1,600.
2. 3,812 people are seated in a concert hall. There are 48 seats in each row. Estimate the number of rows of seats that are occupied. The textbook calculation shows
that in this problem that 3,812 is rounded to 4,000. Why aren't they both rounded to the nearest hundred?
 
I have no idea why they might be rounding differently. But also, I have no idea why they would think it was possible to estimate the number of rows occupied, at all. There could be at least one person in every row! Were you told anything you left out? Can you show the rest of the work?
 
There is no reason in the sense of a firm rule. It would not be wrong to replace 3800 for 3812. But 4000 is less than 5% from 3812 so the resulting error from calculating with that is not large. Furthermore, mental division is hard. It is slightly easier to compute in your head

[MATH]4000 \div 50 = 400 \div 5 = 80 = 10 * 40 \div 5 = 2 * 40 = 80[/MATH]
than

[MATH]3800 \div 50 = 380 \div 5 = 10 * 38 \div 5 = 2 * 38 = 76.[/MATH]
The answer (correct to one decimal point) is

[MATH]3812 \div 48 = 79.4.[/MATH]
Approximation is about making things easy without making big errors.
 
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I focused to much last time on the fact that the second question is misleading. There is really a simple answer to your specific question: when you estimate a quotient, you don't just want fewer digits; you want what are called compatible numbers, because as has been said, division is hard. Once you have decided to round the divisor to 50, you want to round the dividend to a nice multiple of that. That's what they did.
 
I think the first problem was rounded to two significant digits and the second question was rounded to one significant digit.
 
Subhotosh

We cannot know that without knowing what the suggested answers were. If I were doing this with fifth graders, I'd round everything to multiples of ten or a power of ten and have no decimals at all. At worst, I might round one number to a multiple of 5.

Of course, if they are approximating with numbers that are small enough that decimals are significant, I'd change my tune.

[MATH]2.2 \times 1.4 \approx 2 \times 1.5 = 3.[/MATH]
The exact answer of course is [MATH]3.08.[/MATH]
 
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