I found a very simple yet confusing problem

[Megraj]

If 30kg rice costs 50 what is the price of 90kg.
Well, the question is simple but the answer is insatisfactory. There are two possible answers. Through unitary method, the answer is 149 but through adding 50 three times it comes 150(90kg =30+30+30). Though the difference is not much, it is still a flaw

 

[topsquark]

Can you show us the "unitary method?" I don't understand how 149 (however close to 150) would be correct.

-Dan

 

[JeffM]

By any chance are you going

[math]\dfrac{90 \text { kg}}{1} * \dfrac{50 \text { money units}}{30 \text { kg}} = 3 * 50 - 1 = 149[/math]
If so, that is using dimensional analysis incorrectly. The correct way divides by 1 rather than subtracting 1.

[math]\dfrac{90 \text { kg}}{1} * \dfrac{50 \text { money units}}{30 \text {kg}} = \dfrac{3 * \cancel { 30 \text { kg}} * 50 \text { money units}}{1 * \cancel {30 \text { kg}}} =\\ \dfrac{3 * 50}{1} \text { money units} = 150 \text { money units}[/math]

 

[Deleted member 4993]

......................−1

How did that -1 come in?

Can you show us the "unitary method?"

I guess this was the method that I was in secondary school. At that time it was called "rule of three". It went like this:

30kg rice costs = 50 rupees

(30/30 =) 1 kg rice costs = (50/30 =) 5/3 rupees............................make LHS 1

(1 * 90=) 90 kg of rice costs = (5/3 * 90) = 150 rupees .............................(it does not give an answer of 149)

 

[AvgStudent]

If 30kg rice costs 50 what is the price of 90kg.
Well, the question is simple but the answer is insatisfactory. There are two possible answers. Through unitary method, the answer is 149 but through adding 50 three times it comes 150(90kg =30+30+30). Though the difference is not much, it is still a flaw

One potential rounding error I can see. [imath]\dfrac{5}{3} =1.66[/imath] instead of [imath]1.67[/imath]. So [imath]1.66\times 90 =149.4[/imath]

 

[Deleted member 4993]

One potential rounding error I can see. [imath]\dfrac{5}{3} =1.66[/imath] instead of [imath]1.67[/imath]. So [imath]1.66\times 90 =149.4[/imath]

I think your diagnosis of the problem is correct - unnecessary use of calculator and improper rounding in the middle of calculation.

 

[Steven G]

I think your diagnosis of the problem is correct - unnecessary use of calculator and improper rounding in the middle of calculation.

When will students learn that the calculator makes you brain dead after awhile. I am very quick with multiplying even a 2 digit number by a three digit number because I don't use a calculator. If I did use a calculator all the time I too would not know for example what 7*9 equals.

 

[Steven G]

One potential rounding error I can see. [imath]\dfrac{5}{3} =1.66[/imath] instead of [imath]1.67[/imath]. So [imath]1.66\times 90 =149.4[/imath]

Even using 1.7 will give an error, but you are correct that using 1.67 is better and probably correct about why the student got 149.

 

[Megraj]

Can you show us the "unitary method?" I don't understand how 149 (however close to 150) would be correct.

-Dan

Here,
If 30kg = 50
1kg = 50/30
90kg = 50/30 × 90

 

[topsquark]

Here,
If 30kg = 50
1kg = 50/30
90kg = 50/30 × 90

Actually, I was looking for the method that gave the 149.

-Dan

 

[Megraj]

Actually, I was looking for the method that gave the 149.

-Dan

1kg = 50/30= 1.66
90kg = 1.66 × 90 = 149

 

[JeffM]

1kg = 50/30= 1.66
90kg = 1.66 × 90 = 149

And you never realized that 50/30 DOES NOT EQUAL 1.66. It is an approximation that will never give you exact results. We teach students how to be idiots.

 

[topsquark]

1kg = 50/30= 1.66
90kg = 1.66 × 90 = 149

When using a calculator always keep a bunch of extra digits to avoid rounding errors. I use the decimal expression given by the calculator (some 10 digits) and only round the final answer.

-Dan

 

[AvgStudent]

1kg = 50/30= 1.66
90kg = 1.66 × 90 = 149

Hi @Megraj,
If the last digit is less than 5, round the previous digit down. However, if it’s 5 or more then you should round the previous digit up.
5/3=1.666....
If you were going to round this number to 3 significant figures, the 4th digit is 6 so you need to round up the 3rd significant digit to a 7.
[imath]5/3\approx 1.67[/imath] and [imath]1.67\times 90 = 150.3[/imath] which gives you a closer approximation than 1.66.
However, I've learned that it's always best not to round the intermediate steps and wait until the final answer. Hope this helps.

 

[JeffM]

When using a calculator always keep a bunch of extra digits to avoid rounding errors. I use the decimal expression given by the calculator (some 10 digits) and only round the final answer.

-Dan

Yes. 8 or 9 digits of accuracy is usually enough, but it was amazing to me that, in a long financial career, I observed how many people in high financial positions had no clue about sensitivity to errors

Revenue = 1000 [imath]\pm[/imath] 10 Error no greater than 1%.
Expense = 900 [imath]\pm[/imath] 9 Error no greater than 1%.

Profit = Revenue - Expense = 1000 - 900 = 100 [imath]\pm[/imath] 19. It is rare that projected revenue and expense can be estimate within 1%. That that may generate uncertainty of almost 20% in estimated profit is simply flabbergasting to most financial people.

 

[topsquark]

Yes. 8 or 9 digits of accuracy is usually enough, but it was amazing to me that, in a long financial career, I observed how many people in high financial positions had no clue about sensitivity to errors

Revenue = 1000 [imath]\pm[/imath] 10 Error no greater than 1%.
Expense = 900 [imath]\pm[/imath] 9 Error no greater than 1%.

Profit = Revenue - Expense = 1000 - 900 = 100 [imath]\pm[/imath] 19. It is rare that projected revenue and expense can be estimate within 1%. That that may generate uncertainty of almost 20% in estimated profit is simply flabbergasting to most financial people.

And hence all of those stories about computer gurus syphoning the round off errors into their paychecks.

-Dan