Young's modulus question with answer notation issue

[chriscarson]

Summary:: why this answer ?

I have the result of a young s modulus that is 358280256.25 and the answer the teacher gave us is 3.58 x 10 to the power of 8 .

why not 358.3 x 10 to the power of 6 ?

how she s deciding how many steps goes back with the point , the answer of a sum before this one she moved 6 steps back but now 8 .

Any rules please ? thanks

 

[berkeman]

Either way should be fine. The way that you posted with an exponent that is a multiple of "3" is called "Engineering Notation", since it can be represented by a prefix on the units (like kOhm = 10^3 Ohms, MPascal = 10^6 Pascals, etc.).

https://en.wikipedia.org/wiki/Engineering_notation

 

[chriscarson]

Either way should be fine. The way that you posted with an exponent that is a multiple of "3" is called "Engineering Notation", since it can be represented by a prefix on the units (like kOhm = 10^3 Ohms, MPascal = 10^6 Pascals, etc.).

https://en.wikipedia.org/wiki/Engineering_notation

View attachment 256549

what you mean by ( exponent that is a multiple of "3") ?

ok so I should nt have a wrong answer in the exams , I can go back with the point how many steps I want .

Thanks

 

[Merlin3189]

Here in UK, the mantissa with a single non-zero figure before the point multiplied by the appropriate power of ten, is known as "standard form" and is generally used in school science and GCSE exams.
https://gcseguide.co.uk/maths/numbers/standard-form/

 

[berkeman]

what you mean by ( exponent that is a multiple of "3") ?

Did you see the table from Wikipedia that I quoted?

ok so I should nt have a wrong answer in the exams , I can go back with the point how many steps I want .

I'm not able to parse what you said, but as @Merlin3189 points out, your teacher may be wanting to see the answer in standard/scientific notation. Your calculator probably has a configuration to use either notation (mine does, and I keep it in Engineering Notation, since I work with the SI prefixes a lot in my EE work).

 

[chriscarson]

Here in UK, the mantissa with a single non-zero figure before the point multiplied by the appropriate power of ten, is known as "standard form" and is generally used in school science and GCSE exams.
https://gcseguide.co.uk/maths/numbers/standard-form/

I will try that when I buy a scientific calculator . so 10 exp and the number of power is for a number that the point is forward a + i mean , what you press after exp if it is with - the power of ?

 

[chriscarson]

Did you see the table from Wikipedia that I quoted?

I'm not able to parse what you said, but as @Merlin3189 points out, your teacher may be wanting to see the answer in standard/scientific notation. Your calculator probably has a configuration to use either notation (mine does, and I keep it in Engineering Notation, since I work with the SI prefixes a lot in my EE work).

I checked it out but it does nt say if there is standard rule how many steps you go back or forward.

 

[berkeman]

We just told you. The two prominent standards are Engineering Notation (10^3n) and Scientific Notation.

https://en.wikipedia.org/wiki/Engineering_notation
'
https://en.wikipedia.org/wiki/Scientific_notation

What calculator do you use?

 

[chriscarson]

We just told you. The two prominent standards are Engineering Notation (10^3n) and Scientific Notation.

https://en.wikipedia.org/wiki/Engineering_notation
'
https://en.wikipedia.org/wiki/Scientific_notation

What calculator do you use?

just a simple one , not scientific

 

[berkeman]

A simple calculator will likely not include the Engineering Notation option.

What does it display if you do this: 1,000,000 squared?

 

[chriscarson]

A simple calculator will likely not include the Engineering Notation option.

What does it display if you do this: 1,000,000 squared?

1 000

 

[berkeman]

1 000

Squared. Not square root...

 

[chriscarson]

Squared. Not square root...

oh sorry , I think I don t have that button

 

[berkeman]

So on my HP42 scientific calculator (on my Droid smartphone), I get these answers:

Engineering Notation:
(1,000,000)^2 = 1.00E12
(4,000,000)^2 = 16.0E12

Scientific Notation:
(1,000,000)^2 = 1.00E12
(4,000,000)^2 = 1.60E13

Makes sense?

 

[berkeman]

oh sorry , I think I don t have that button

Then just type 1,000,000 X 1,000,000 and so on...

 

[chriscarson]

So on my HP42 scientific calculator (on my Droid smartphone), I get these answers:

Engineering Notation:
(1,000,000)^2 = 1.00E12
(4,000,000)^2 = 16.0E12

Scientific Notation:
(1,000,000)^2 = 1.00E12
(4,000,000)^2 = 1.60E13

Makes sense?

sorry but I don t understand that much about physics , well we don t have to go that deep I guess but maybe in the future I will meet this table , I will keep it , thanks

 

[BvU]

358280256.25

When I see a number like that I've been taught to read that the actual value is between
358280256.245 and 358280256.255 and the relative accuracy would be around 10^-10. Probably too optimistic.

Apparently teacher knows that the accuracy of the given data justifies around three digits, no more.

[edit] forgot to post -- my reply has been sitting here for hours :-)

 

[Cutter Ketch]

Summary:: why this answer ?

I have the result of a young s modulus that is 358280256.25 and the answer the teacher gave us is 3.58 x 10 to the power of 8 .

why not 358.3 x 10 to the power of 6 ?

how she s deciding how many steps goes back with the point , the answer of a sum before this one she moved 6 steps back but now 8 .

Any rules please ? thanks

No one should ever be marked wrong for this choice of notation. Yes, scientific is pretty standard, and yes engineering is another common choice. Yes, you will communicate best and annoy the least if you conform. However all choices are easily understood as the same number. You just can’t say that the answer is wrong unless the notation is what you are teaching and the problem says to “write the answer in standard form” or similar. Short of that, the right number is the right number no matter how you write it.

On the other hand the two forms you give in the original post have different numbers of significant figures, and getting that wrong can easily lead to losing some points. Are you sure you lost points for notation, or might you have lost points for significant figures?

 

[chriscarson]

When I see a number like that I've been taught to read that the actual value is between
358280256.245 and 358280256.255 and the relative accuracy would be around 10^-10. Probably too optimistic.

Apparently teacher knows that the accuracy of the given data justifies around three digits, no more.

[edit] forgot to post -- my reply has been sitting here for hours :-)

Yes maybe this time with 3 digits but later on or before she used 2 digits before the point .

 

[chriscarson]

No one should ever be marked wrong for this choice of notation. Yes, scientific is pretty standard, and yes engineering is another common choice. Yes, you will communicate best and annoy the least if you conform. However all choices are easily understood as the same number. You just can’t say that the answer is wrong unless the notation is what you are teaching and the problem says to “write the answer in standard form” or similar. Short of that, the right number is the right number no matter how you write it.

On the other hand the two forms you give in the original post have different numbers of significant figures, and getting that wrong can easily lead to losing some points. Are you sure you lost points for notation, or might you have lost points for significant figures?

No I just asked if I will lose marks .