Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Find Number of Revolutions

How many revolutions will a circular disk with a diameter of 4 feet have completed after it has rolled 20 feet?

Let me see.

C = pi•d

C = 3.14159265359 • 4

C = 12.56637061436

Round to two decimal places.

C = 12.57

Let R = revolutions I need to find.

R = (20 feet)/(12.57)

R = 1.59

Round to the first unit.

R = 2

Is this right?

Last edited by mathxyz (2024-05-16 13:34:16)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Find Number of Revolutions

Yes, that answer is OK. But, a word of warning. If a calculation has, let's say, 2 stages and you round off after stage 1, using that result for stage 2, it could happen that the final answer is different from what you would get if you only round off once at the end of stage 2.

In UK exams, candidates are advised to maintain full accuracy until the end and then to round to a sensible number of figures based on the accuracy of the initial values and the precision of the model.

Some years ago I had a dispute with my gas supplier about the bill. Their calculation had four stages and they were rounding off after each stage. The final figure was 'wrong' by a considerable amount.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Number of Revolutions

Yes, that answer is OK. But, a word of warning. If a calculation has, let's say, 2 stages and you round off after stage 1, using that result for stage 2, it could happen that the final answer is different from what you would get if you only round off once at the end of stage 2.

In UK exams, candidates are advised to maintain full accuracy until the end and then to round to a sensible number of figures based on the accuracy of the initial values and the precision of the model.

Some years ago I had a dispute with my gas supplier about the bill. Their calculation had four stages and they were rounding off after each stage. The final figure was 'wrong' by a considerable amount.

Bob

Wow! I did not know this truth about calculations. In the United States, we are told the opposite. I recall a few math teachers back in my school days instructing the class to round off as soon as we get a chance to do so. Now, what would be another answer to this revolution problem if I decided to leave rounding for last?

United States education has been on a decline for decades. For example, in NYC public schools, it is more about filling in the hole in terms of teachers than hiring the right person for the job. During my 8 years a substitute teacher, I vividly recall gym teachers hired to teach math, music teachers hired to teach history, science teachers hired to teach typing, etc. It is called OUT-OF-SUBJECT TEACHING. The students suffer in the long run big time. They don't care about students because it is all about the money, political corruption and greed.

Last edited by mathxyz (2024-05-17 03:40:07)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Find Number of Revolutions

I did try to find a good example of why my advice is right.  It'll take a bit of trial and error but an example is lurking out there for me.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Number of Revolutions

I did try to find a good example of why my advice is right.  It'll take a bit of trial and error but an example is lurking out there for me.

Bob

Ok. I am anxious to see an example.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Find Number of Revolutions

The circumference of a circle is 30.  Work out the area.

There are two steps here: (1) calculate the radius (2) calculate the area

If I round this off to 5 then

If I keep the full accuracy for r

That's quite a difference.  The error is made worse because r is being squared which magnifies the error.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Number of Revolutions

The circumference of a circle is 30.  Work out the area.

There are two steps here: (1) calculate the radius (2) calculate the area

If I round this off to 5 then

If I keep the full accuracy for r

That's quite a difference.  The error is made worse because r is being squared which magnifies the error.

Bob

Thank you for the math work. This revolution problem in on page 37 problem 46.