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Why do I get badly formatted numerical results when I use StringForm?
The 2019 Stack Overflow Developer Survey Results Are InHow to display a different number of significant digits in each column of TableForm output?Prevent graphics from rendering inside a held expressionHow to update Print-out “in place”?NumberForm pesky warning from ManipulateHow to separately define TraditionalForm and TeXFormPreventing Mathematica from simplifying numbers under the root?How to display numbers as multiples of a square rootPrinting out reals in a table with a specified number of digitsPadding a number doesn't work when transferring to LaTeXHandling expression differently for display vs. calculation?
$begingroup$
The following example prints the square and cube of numbers from 0.5 to 6
Do[
Print[StringForm["the square of `` is ``, the cube of it is ``", i, i^2, i^3]],
i, 0.5, 6, 0.1]
It should be fine, however, for 0.7 Mathematica prints
the square of 0.7` is 0.48999999999999994`, the cube of it is 0.3429999999999999`
Why is the square of 0.7 approximated by 0.48999999999999994? No approximation will be made if I did not use StringForm
, why is that?
By the way, there is a ` at the end of each output number, why is it there?
output-formatting number-form
$endgroup$
add a comment |
$begingroup$
The following example prints the square and cube of numbers from 0.5 to 6
Do[
Print[StringForm["the square of `` is ``, the cube of it is ``", i, i^2, i^3]],
i, 0.5, 6, 0.1]
It should be fine, however, for 0.7 Mathematica prints
the square of 0.7` is 0.48999999999999994`, the cube of it is 0.3429999999999999`
Why is the square of 0.7 approximated by 0.48999999999999994? No approximation will be made if I did not use StringForm
, why is that?
By the way, there is a ` at the end of each output number, why is it there?
output-formatting number-form
$endgroup$
add a comment |
$begingroup$
The following example prints the square and cube of numbers from 0.5 to 6
Do[
Print[StringForm["the square of `` is ``, the cube of it is ``", i, i^2, i^3]],
i, 0.5, 6, 0.1]
It should be fine, however, for 0.7 Mathematica prints
the square of 0.7` is 0.48999999999999994`, the cube of it is 0.3429999999999999`
Why is the square of 0.7 approximated by 0.48999999999999994? No approximation will be made if I did not use StringForm
, why is that?
By the way, there is a ` at the end of each output number, why is it there?
output-formatting number-form
$endgroup$
The following example prints the square and cube of numbers from 0.5 to 6
Do[
Print[StringForm["the square of `` is ``, the cube of it is ``", i, i^2, i^3]],
i, 0.5, 6, 0.1]
It should be fine, however, for 0.7 Mathematica prints
the square of 0.7` is 0.48999999999999994`, the cube of it is 0.3429999999999999`
Why is the square of 0.7 approximated by 0.48999999999999994? No approximation will be made if I did not use StringForm
, why is that?
By the way, there is a ` at the end of each output number, why is it there?
output-formatting number-form
output-formatting number-form
edited yesterday
m_goldberg
88.6k873200
88.6k873200
asked 2 days ago
zyyzyy
1286
1286
add a comment |
add a comment |
4 Answers
4
active
oldest
votes
$begingroup$
This is what happens when you use IEEE-754 double-precision math instead of exact math.
StringForm
, InputForm
, FullForm
etc. give you all possible digits of these IEEE-754 double-precision numbers used internally. This is no different from any other programming language.
Other number display functions, like NumberForm
, show fewer digits. The internal representation of the number doesn't change though.
The backtick ` indicates a machine-precision number, which is usually (always?) an IEEE-754 double-precision number.
You can get the result you're looking for by doing the conversion to numerical values after the squaring/cubing:
Do[Print[StringForm["the square of `` is ``, the cube of it is ``",
N[i], N[i^2], N[i^3]]], i, 1/2, 6, 1/10]
the square of 0.7` is 0.49`, the cube of it is 0.343`
$endgroup$
add a comment |
$begingroup$
StringForm
is very old. It goes all the back to V1.0, released in 1988. It represents an attempt by WRI to have an IO formatter that would appeal to programmers familiar with C and similar programming languages.
V6.0, released in 2003, added formatting tools that are not only easier to use but which are better integrated into Mathematica's way of doing things. One of the new IO formatters was Row
. It does not have the problem with formatting machine numbers that you ran into by using StringForm
.
Here is how you can get your output with Row
.
Column[
Table[
Row["the square of ", i, " is ", i^2, ", the cube of it is ", i^3],
i, 0.5, 1., .1]]
One of the nice features of the newer IO formatting tools is that they allow styles to be applied at almost any level. For example:
numStyle[num_?NumericQ] := Style[num, Red, Bold, Italic]
Style[
Column[
Table[
Row[
"the square of ", numStyle[i], " is ", numStyle[i^2],
", the cube of it is ", numStyle[i^3]],
i, 0.5, 1., .1]],
FontFamily -> "Arial"]
It isn't that you can't apply styles to StringForm
output, but that it is harder to do and requires more care.
$endgroup$
add a comment |
$begingroup$
I would recommend looking at StringTemplate
.
Do[Print[StringTemplate[
"the square of `` is ``, the cube of it is ``"][i, i^2, i^3]], i,
0.5, 1, 0.1]
the square of 0.5 is 0.25, the cube of it is 0.125
the square of 0.6 is 0.36, the cube of it is 0.216
the square of 0.7 is 0.49, the cube of it is 0.343
the square of 0.8 is 0.64, the cube of it is 0.512
the square of 0.9 is 0.81, the cube of it is 0.729
the square of 1. is 1., the cube of it is 1.
$endgroup$
add a comment |
$begingroup$
You can also use StandardForm
, which is the standard format of output cells:
Do[Print[StringForm["the square of `` is ``, the cube of it is ``",
StandardForm[i], StandardForm[i^2], StandardForm[i^3]]],
i, 0.5, 6, 0.1]
$endgroup$
add a comment |
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
This is what happens when you use IEEE-754 double-precision math instead of exact math.
StringForm
, InputForm
, FullForm
etc. give you all possible digits of these IEEE-754 double-precision numbers used internally. This is no different from any other programming language.
Other number display functions, like NumberForm
, show fewer digits. The internal representation of the number doesn't change though.
The backtick ` indicates a machine-precision number, which is usually (always?) an IEEE-754 double-precision number.
You can get the result you're looking for by doing the conversion to numerical values after the squaring/cubing:
Do[Print[StringForm["the square of `` is ``, the cube of it is ``",
N[i], N[i^2], N[i^3]]], i, 1/2, 6, 1/10]
the square of 0.7` is 0.49`, the cube of it is 0.343`
$endgroup$
add a comment |
$begingroup$
This is what happens when you use IEEE-754 double-precision math instead of exact math.
StringForm
, InputForm
, FullForm
etc. give you all possible digits of these IEEE-754 double-precision numbers used internally. This is no different from any other programming language.
Other number display functions, like NumberForm
, show fewer digits. The internal representation of the number doesn't change though.
The backtick ` indicates a machine-precision number, which is usually (always?) an IEEE-754 double-precision number.
You can get the result you're looking for by doing the conversion to numerical values after the squaring/cubing:
Do[Print[StringForm["the square of `` is ``, the cube of it is ``",
N[i], N[i^2], N[i^3]]], i, 1/2, 6, 1/10]
the square of 0.7` is 0.49`, the cube of it is 0.343`
$endgroup$
add a comment |
$begingroup$
This is what happens when you use IEEE-754 double-precision math instead of exact math.
StringForm
, InputForm
, FullForm
etc. give you all possible digits of these IEEE-754 double-precision numbers used internally. This is no different from any other programming language.
Other number display functions, like NumberForm
, show fewer digits. The internal representation of the number doesn't change though.
The backtick ` indicates a machine-precision number, which is usually (always?) an IEEE-754 double-precision number.
You can get the result you're looking for by doing the conversion to numerical values after the squaring/cubing:
Do[Print[StringForm["the square of `` is ``, the cube of it is ``",
N[i], N[i^2], N[i^3]]], i, 1/2, 6, 1/10]
the square of 0.7` is 0.49`, the cube of it is 0.343`
$endgroup$
This is what happens when you use IEEE-754 double-precision math instead of exact math.
StringForm
, InputForm
, FullForm
etc. give you all possible digits of these IEEE-754 double-precision numbers used internally. This is no different from any other programming language.
Other number display functions, like NumberForm
, show fewer digits. The internal representation of the number doesn't change though.
The backtick ` indicates a machine-precision number, which is usually (always?) an IEEE-754 double-precision number.
You can get the result you're looking for by doing the conversion to numerical values after the squaring/cubing:
Do[Print[StringForm["the square of `` is ``, the cube of it is ``",
N[i], N[i^2], N[i^3]]], i, 1/2, 6, 1/10]
the square of 0.7` is 0.49`, the cube of it is 0.343`
edited 2 days ago
answered 2 days ago
RomanRoman
5,06011130
5,06011130
add a comment |
add a comment |
$begingroup$
StringForm
is very old. It goes all the back to V1.0, released in 1988. It represents an attempt by WRI to have an IO formatter that would appeal to programmers familiar with C and similar programming languages.
V6.0, released in 2003, added formatting tools that are not only easier to use but which are better integrated into Mathematica's way of doing things. One of the new IO formatters was Row
. It does not have the problem with formatting machine numbers that you ran into by using StringForm
.
Here is how you can get your output with Row
.
Column[
Table[
Row["the square of ", i, " is ", i^2, ", the cube of it is ", i^3],
i, 0.5, 1., .1]]
One of the nice features of the newer IO formatting tools is that they allow styles to be applied at almost any level. For example:
numStyle[num_?NumericQ] := Style[num, Red, Bold, Italic]
Style[
Column[
Table[
Row[
"the square of ", numStyle[i], " is ", numStyle[i^2],
", the cube of it is ", numStyle[i^3]],
i, 0.5, 1., .1]],
FontFamily -> "Arial"]
It isn't that you can't apply styles to StringForm
output, but that it is harder to do and requires more care.
$endgroup$
add a comment |
$begingroup$
StringForm
is very old. It goes all the back to V1.0, released in 1988. It represents an attempt by WRI to have an IO formatter that would appeal to programmers familiar with C and similar programming languages.
V6.0, released in 2003, added formatting tools that are not only easier to use but which are better integrated into Mathematica's way of doing things. One of the new IO formatters was Row
. It does not have the problem with formatting machine numbers that you ran into by using StringForm
.
Here is how you can get your output with Row
.
Column[
Table[
Row["the square of ", i, " is ", i^2, ", the cube of it is ", i^3],
i, 0.5, 1., .1]]
One of the nice features of the newer IO formatting tools is that they allow styles to be applied at almost any level. For example:
numStyle[num_?NumericQ] := Style[num, Red, Bold, Italic]
Style[
Column[
Table[
Row[
"the square of ", numStyle[i], " is ", numStyle[i^2],
", the cube of it is ", numStyle[i^3]],
i, 0.5, 1., .1]],
FontFamily -> "Arial"]
It isn't that you can't apply styles to StringForm
output, but that it is harder to do and requires more care.
$endgroup$
add a comment |
$begingroup$
StringForm
is very old. It goes all the back to V1.0, released in 1988. It represents an attempt by WRI to have an IO formatter that would appeal to programmers familiar with C and similar programming languages.
V6.0, released in 2003, added formatting tools that are not only easier to use but which are better integrated into Mathematica's way of doing things. One of the new IO formatters was Row
. It does not have the problem with formatting machine numbers that you ran into by using StringForm
.
Here is how you can get your output with Row
.
Column[
Table[
Row["the square of ", i, " is ", i^2, ", the cube of it is ", i^3],
i, 0.5, 1., .1]]
One of the nice features of the newer IO formatting tools is that they allow styles to be applied at almost any level. For example:
numStyle[num_?NumericQ] := Style[num, Red, Bold, Italic]
Style[
Column[
Table[
Row[
"the square of ", numStyle[i], " is ", numStyle[i^2],
", the cube of it is ", numStyle[i^3]],
i, 0.5, 1., .1]],
FontFamily -> "Arial"]
It isn't that you can't apply styles to StringForm
output, but that it is harder to do and requires more care.
$endgroup$
StringForm
is very old. It goes all the back to V1.0, released in 1988. It represents an attempt by WRI to have an IO formatter that would appeal to programmers familiar with C and similar programming languages.
V6.0, released in 2003, added formatting tools that are not only easier to use but which are better integrated into Mathematica's way of doing things. One of the new IO formatters was Row
. It does not have the problem with formatting machine numbers that you ran into by using StringForm
.
Here is how you can get your output with Row
.
Column[
Table[
Row["the square of ", i, " is ", i^2, ", the cube of it is ", i^3],
i, 0.5, 1., .1]]
One of the nice features of the newer IO formatting tools is that they allow styles to be applied at almost any level. For example:
numStyle[num_?NumericQ] := Style[num, Red, Bold, Italic]
Style[
Column[
Table[
Row[
"the square of ", numStyle[i], " is ", numStyle[i^2],
", the cube of it is ", numStyle[i^3]],
i, 0.5, 1., .1]],
FontFamily -> "Arial"]
It isn't that you can't apply styles to StringForm
output, but that it is harder to do and requires more care.
edited yesterday
answered yesterday
m_goldbergm_goldberg
88.6k873200
88.6k873200
add a comment |
add a comment |
$begingroup$
I would recommend looking at StringTemplate
.
Do[Print[StringTemplate[
"the square of `` is ``, the cube of it is ``"][i, i^2, i^3]], i,
0.5, 1, 0.1]
the square of 0.5 is 0.25, the cube of it is 0.125
the square of 0.6 is 0.36, the cube of it is 0.216
the square of 0.7 is 0.49, the cube of it is 0.343
the square of 0.8 is 0.64, the cube of it is 0.512
the square of 0.9 is 0.81, the cube of it is 0.729
the square of 1. is 1., the cube of it is 1.
$endgroup$
add a comment |
$begingroup$
I would recommend looking at StringTemplate
.
Do[Print[StringTemplate[
"the square of `` is ``, the cube of it is ``"][i, i^2, i^3]], i,
0.5, 1, 0.1]
the square of 0.5 is 0.25, the cube of it is 0.125
the square of 0.6 is 0.36, the cube of it is 0.216
the square of 0.7 is 0.49, the cube of it is 0.343
the square of 0.8 is 0.64, the cube of it is 0.512
the square of 0.9 is 0.81, the cube of it is 0.729
the square of 1. is 1., the cube of it is 1.
$endgroup$
add a comment |
$begingroup$
I would recommend looking at StringTemplate
.
Do[Print[StringTemplate[
"the square of `` is ``, the cube of it is ``"][i, i^2, i^3]], i,
0.5, 1, 0.1]
the square of 0.5 is 0.25, the cube of it is 0.125
the square of 0.6 is 0.36, the cube of it is 0.216
the square of 0.7 is 0.49, the cube of it is 0.343
the square of 0.8 is 0.64, the cube of it is 0.512
the square of 0.9 is 0.81, the cube of it is 0.729
the square of 1. is 1., the cube of it is 1.
$endgroup$
I would recommend looking at StringTemplate
.
Do[Print[StringTemplate[
"the square of `` is ``, the cube of it is ``"][i, i^2, i^3]], i,
0.5, 1, 0.1]
the square of 0.5 is 0.25, the cube of it is 0.125
the square of 0.6 is 0.36, the cube of it is 0.216
the square of 0.7 is 0.49, the cube of it is 0.343
the square of 0.8 is 0.64, the cube of it is 0.512
the square of 0.9 is 0.81, the cube of it is 0.729
the square of 1. is 1., the cube of it is 1.
answered yesterday
chuychuy
9,4731841
9,4731841
add a comment |
add a comment |
$begingroup$
You can also use StandardForm
, which is the standard format of output cells:
Do[Print[StringForm["the square of `` is ``, the cube of it is ``",
StandardForm[i], StandardForm[i^2], StandardForm[i^3]]],
i, 0.5, 6, 0.1]
$endgroup$
add a comment |
$begingroup$
You can also use StandardForm
, which is the standard format of output cells:
Do[Print[StringForm["the square of `` is ``, the cube of it is ``",
StandardForm[i], StandardForm[i^2], StandardForm[i^3]]],
i, 0.5, 6, 0.1]
$endgroup$
add a comment |
$begingroup$
You can also use StandardForm
, which is the standard format of output cells:
Do[Print[StringForm["the square of `` is ``, the cube of it is ``",
StandardForm[i], StandardForm[i^2], StandardForm[i^3]]],
i, 0.5, 6, 0.1]
$endgroup$
You can also use StandardForm
, which is the standard format of output cells:
Do[Print[StringForm["the square of `` is ``, the cube of it is ``",
StandardForm[i], StandardForm[i^2], StandardForm[i^3]]],
i, 0.5, 6, 0.1]
answered yesterday
Michael E2Michael E2
150k12203482
150k12203482
add a comment |
add a comment |
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