Mixing
If one rounds digits one by one starting from the end, then is the rounding same as when “cut-offing†around required the precision?
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If one rounds digits one by one starting from the end, then is the rounding same as when "cut-offing" around required the precision?
That is does (for $1/10^3$):
$0.84562...4356 rightarrow 0.8456 rightarrow 0.846$
produce the same as
$0.84562...4356 rightarrow 0.84562...436$
$ rightarrow 0.84562...44 rightarrow 0.84562...4$
up until: $rightarrow 0.846$
approximation
asked Aug 6 at 8:58
mavavilj
2,470730
add a comment |Â
up vote
0
down vote
favorite
If one rounds digits one by one starting from the end, then is the rounding same as when "cut-offing" around required the precision?
That is does (for $1/10^3$):
$0.84562...4356 rightarrow 0.8456 rightarrow 0.846$
produce the same as
$0.84562...4356 rightarrow 0.84562...436$
$ rightarrow 0.84562...44 rightarrow 0.84562...4$
up until: $rightarrow 0.846$
approximation
asked Aug 6 at 8:58
mavavilj
2,470730
How does $44$ become $5$?
– Arnaud Mortier
Aug 6 at 9:26
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If one rounds digits one by one starting from the end, then is the rounding same as when "cut-offing" around required the precision?
That is does (for $1/10^3$):
$0.84562...4356 rightarrow 0.8456 rightarrow 0.846$
produce the same as
$0.84562...4356 rightarrow 0.84562...436$
$ rightarrow 0.84562...44 rightarrow 0.84562...4$
up until: $rightarrow 0.846$
approximation
asked Aug 6 at 8:58
mavavilj
2,470730
If one rounds digits one by one starting from the end, then is the rounding same as when "cut-offing" around required the precision?
That is does (for $1/10^3$):
$0.84562...4356 rightarrow 0.8456 rightarrow 0.846$
produce the same as
$0.84562...4356 rightarrow 0.84562...436$
$ rightarrow 0.84562...44 rightarrow 0.84562...4$
up until: $rightarrow 0.846$
approximation
asked Aug 6 at 8:58
mavavilj
2,470730
edited Aug 6 at 9:29
asked Aug 6 at 8:58
mavavilj
2,470730
asked Aug 6 at 8:58
mavavilj
2,470730
asked Aug 6 at 8:58
mavavilj
2,470730
2,470730
How does $44$ become $5$?
– Arnaud Mortier
Aug 6 at 9:26
add a comment |Â
How does $44$ become $5$?
– Arnaud Mortier
Aug 6 at 9:26
How does $44$ become $5$?
– Arnaud Mortier
Aug 6 at 9:26
How does $44$ become $5$?
– Arnaud Mortier
Aug 6 at 9:26
add a comment |Â
1 Answer
1
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votes
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0
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No, you cant't use these methods equivalently.
For example by the sequence of rounding we have:
$$.846 approx .85 approx .9$$
while the single rounding (which is the proper method) gives us:
$$.846 approx .8$$
answered Aug 6 at 9:11
Jaroslaw Matlak
3,880830
So how did they figure out the cutoff method as the valid one? Particularly, what's the property that makes it valid and the other invalid?
– mavavilj
Aug 6 at 9:14
See the approximation error. In "cut off" method it is smaller. In sequentional rounding the approximation error accumulates and then it can be higher (like in the example above).
– Jaroslaw Matlak
Aug 6 at 9:23
In the other words - in each step of the step-by-step rounding, you approximate different number. In most cases it would give you the same result, but when the number is close to the half, the results might differ.
– Jaroslaw Matlak
Aug 6 at 9:26
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
No, you cant't use these methods equivalently.
For example by the sequence of rounding we have:
$$.846 approx .85 approx .9$$
while the single rounding (which is the proper method) gives us:
$$.846 approx .8$$
answered Aug 6 at 9:11
Jaroslaw Matlak
3,880830
So how did they figure out the cutoff method as the valid one? Particularly, what's the property that makes it valid and the other invalid?
– mavavilj
Aug 6 at 9:14
See the approximation error. In "cut off" method it is smaller. In sequentional rounding the approximation error accumulates and then it can be higher (like in the example above).
– Jaroslaw Matlak
Aug 6 at 9:23
In the other words - in each step of the step-by-step rounding, you approximate different number. In most cases it would give you the same result, but when the number is close to the half, the results might differ.
– Jaroslaw Matlak
Aug 6 at 9:26
add a comment |Â
up vote
0
down vote
No, you cant't use these methods equivalently.
For example by the sequence of rounding we have:
$$.846 approx .85 approx .9$$
while the single rounding (which is the proper method) gives us:
$$.846 approx .8$$
answered Aug 6 at 9:11
Jaroslaw Matlak
3,880830
So how did they figure out the cutoff method as the valid one? Particularly, what's the property that makes it valid and the other invalid?
– mavavilj
Aug 6 at 9:14
See the approximation error. In "cut off" method it is smaller. In sequentional rounding the approximation error accumulates and then it can be higher (like in the example above).
– Jaroslaw Matlak
Aug 6 at 9:23
In the other words - in each step of the step-by-step rounding, you approximate different number. In most cases it would give you the same result, but when the number is close to the half, the results might differ.
– Jaroslaw Matlak
Aug 6 at 9:26
add a comment |Â
up vote
0
down vote
up vote
0
down vote
No, you cant't use these methods equivalently.
For example by the sequence of rounding we have:
$$.846 approx .85 approx .9$$
while the single rounding (which is the proper method) gives us:
$$.846 approx .8$$
answered Aug 6 at 9:11
Jaroslaw Matlak
3,880830
No, you cant't use these methods equivalently.
For example by the sequence of rounding we have:
$$.846 approx .85 approx .9$$
while the single rounding (which is the proper method) gives us:
$$.846 approx .8$$
answered Aug 6 at 9:11
Jaroslaw Matlak
3,880830
edited Aug 6 at 9:16
answered Aug 6 at 9:11
Jaroslaw Matlak
3,880830
answered Aug 6 at 9:11
Jaroslaw Matlak
3,880830
answered Aug 6 at 9:11
Jaroslaw Matlak
3,880830
3,880830
So how did they figure out the cutoff method as the valid one? Particularly, what's the property that makes it valid and the other invalid?
– mavavilj
Aug 6 at 9:14
See the approximation error. In "cut off" method it is smaller. In sequentional rounding the approximation error accumulates and then it can be higher (like in the example above).
– Jaroslaw Matlak
Aug 6 at 9:23
In the other words - in each step of the step-by-step rounding, you approximate different number. In most cases it would give you the same result, but when the number is close to the half, the results might differ.
– Jaroslaw Matlak
Aug 6 at 9:26
add a comment |Â
So how did they figure out the cutoff method as the valid one? Particularly, what's the property that makes it valid and the other invalid?
– mavavilj
Aug 6 at 9:14
See the approximation error. In "cut off" method it is smaller. In sequentional rounding the approximation error accumulates and then it can be higher (like in the example above).
– Jaroslaw Matlak
Aug 6 at 9:23
In the other words - in each step of the step-by-step rounding, you approximate different number. In most cases it would give you the same result, but when the number is close to the half, the results might differ.
– Jaroslaw Matlak
Aug 6 at 9:26
So how did they figure out the cutoff method as the valid one? Particularly, what's the property that makes it valid and the other invalid?
– mavavilj
Aug 6 at 9:14
So how did they figure out the cutoff method as the valid one? Particularly, what's the property that makes it valid and the other invalid?
– mavavilj
Aug 6 at 9:14
See the approximation error. In "cut off" method it is smaller. In sequentional rounding the approximation error accumulates and then it can be higher (like in the example above).
– Jaroslaw Matlak
Aug 6 at 9:23
See the approximation error. In "cut off" method it is smaller. In sequentional rounding the approximation error accumulates and then it can be higher (like in the example above).
– Jaroslaw Matlak
Aug 6 at 9:23
In the other words - in each step of the step-by-step rounding, you approximate different number. In most cases it would give you the same result, but when the number is close to the half, the results might differ.
– Jaroslaw Matlak
Aug 6 at 9:26
In the other words - in each step of the step-by-step rounding, you approximate different number. In most cases it would give you the same result, but when the number is close to the half, the results might differ.
– Jaroslaw Matlak
Aug 6 at 9:26
add a comment |Â
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How does $44$ become $5$?
– Arnaud Mortier
Aug 6 at 9:26