Decimal points different in these two answers

[chriscarson]

Homework Statement

Result in decimal point

Relevant Equations

go back or forward with the point

I have two answers and somehow the answers have the decimal point in different place.

2445859.873 with the answer of 2.44x10⁶

and

254777070.1 with the answer of 254.6x10⁶

why the teacher do that ?

 

[Lnewqban]

Perhaps the teacher wanted to cancel $10^6$ in some operation?

Please, see:
https://en.wikipedia.org/wiki/Scientific_notation

 

[chriscarson]

Perhaps the teacher wanted to cancel $10^6$ in some operation?

Please, see:
https://en.wikipedia.org/wiki/Scientific_notation

I understand why it is used but why 254777070.1 with the answer of 254.6x10⁶ and not 2.55x10⁸?

 

[etotheipi]

2445859.873 with the answer of 2.44x10⁶
and
254777070.1 with the answer of 254.6x10⁶

Your teacher has not rounded those numbers correctly

 

[chriscarson]

Your teacher has not rounded those numbers correctly

we find mistakes in their work so nothing new.

 

[etotheipi]

@chriscarson are $123000$, $123 \times 10^3$ and $1.23 \times 10^5$ all the same number?

 

[Mark44]

I have two answers and somehow the answers have the decimal point in different place.

2445859.873 with the answer of 2.44x10⁶

and

254777070.1 with the answer of 254.6x10⁶

why the teacher do that ?

Were your answers 2445859.873 and 254777070.1?
If the teacher's answers were 2.44x10⁶ and 254.6x10⁶, then I believe that your answers or the teacher's answers might have been slightly off. To three significant digits, 2445859.873 would be 2.45 x 10⁶, and to four significant digits, 254777070.1 would be 254.8 x 10⁶.

As already mentioned, writing both numbers times 10⁶ might have been done for some reason that you didn't mention.

 

[chriscarson]

@chriscarson are $123000$, $123 \times 10^3$ and $1.23 \times 10^5$ all the same number?

so I would have a good answer with both 254.6x10⁶ and 2.55x10⁸ when I have 254777070.1 on the calculator ?

 

[etotheipi]

Assuming you fix the dodgy rounding, then yeah!

 

[Mark44]

so I would have a good answer with both 254.6x10⁶ and 2.55x10⁸ when I have 254777070.1 on the calculator ?

No for your first answer. It would be 254.8x10⁶

 

[chriscarson]

Were your answers 2445859.873 and 254777070.1?
If the teacher's answers were 2.44x10⁶ and 254.6x10⁶, then I believe that your answers or the teacher's answers might have been slightly off. To three significant digits, 2445859.873 would be 2.45 x 10⁶, and to four significant digits, 254777070.1 would be 254.8 x 10⁶.

As already mentioned, writing both numbers times 10⁶ might have been done for some reason that you didn't mention.

yeah probably there is something that she prefers x10⁶ that she doesn t said why.

 

[chriscarson]

No for your first answer. It would be 254.8x10⁶

2.55x10⁸ would also be good ?

 

[Mark44]

2.55x10⁸ would also be good ?

Yes, depending on how many significant figures are required.

 

[chriscarson]

Assuming you fix the dodgy rounding, then yeah!

dodgy I guess you mean the mistake

 

[chriscarson]

Yes, depending on how many significant figures are required.

it s not asked , ok so thanks

 

[chriscarson]

thanks all...

 

[Steve4Physics]

2445859.873 → 2.44x10⁶ is wrong.
2445859.873 → 2.45x10⁶ is correct if rounding to 3 sig. figs.

254777070.1 → 254.6x10⁶ is wrong
254777070.1 → 254.8x10⁶ is correct if rounding to 4 sig. figs.
(But it is not 'standard form' and it would be more usual to express it as 2.548x10⁸ if 4 sig. are required,)

However there might be a reason for using 10⁶ in both cases. If (for example) your initial values were in units of μs and you wanted the final answers in seconds, it would be helpful to use 10⁶ for both. Then the answers would simply be 2.45s and 254.8s

 

[chriscarson]

2445859.873 → 2.44x10⁶ is wrong.
2445859.873 → 2.45x10⁶ is correct if rounding to 3 sig. figs.

254777070.1 → 254.6x10⁶ is wrong
254777070.1 → 254.8x10⁶ is correct if rounding to 4 sig. figs.
(But it is not 'standard form' and it would be more usual to express it as 2.548x10⁸ if 4 sig. are required,)

However there might be a reason for using 10⁶ in both cases. If (for example) your initial values were in units of μs and you wanted the final answers in seconds, it would be helpful to use 10⁶ for both. Then the answers would simply be 2.45s and 254.8s

yes it shows like you are saying , they are both x10⁶, thanks.