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zhulaojianke1-Visitor
1-Visitor
August 27, 2014
Question

How to increase the computational accuracy of mathcad?

  • August 27, 2014
  • 1 reply
  • 6425 views

It seems that the numerical calculation in Mathcad only can process 16 significant figures, such as 123.4567890123456 or 123456789.0123456, and when the number have more significant figures, MC will round it to 16 or 17.

I knew that symbolic calculation could process up to 250 decimal. But I need use it in the programming, and the result of the symbolic calculation can't use in programming.

When I use:

x:=x-trunc(x)

x:=x*10^8-trunc(x*10^8)

to get the number after 10^-8, I get a lot of number irrelevant! Look at the picture below:

2014-08-27_221107.jpg

In my opinion, the result must be 98765432.11234568, but MC return a unacountable number! Is it another bug of MC15?

And how should I do to increase the computational accuracy?

In Mathcad Prime 2.0, the result is same:

2014-08-27_225236.jpg

1 reply

W
Werner_E25-Diamond I
25-Diamond I
August 27, 2014

You wrote yourself that Mathcads numerics is limited to 16 significant digits. Then you define a number with 27 significant digits and you really are surprised that the last 10 or so digits don't show up correctly? I would have been surprised if you would have got the result you expected as this would mean that Mathcads numeric accuracy is much better than what they state in the docs.

What kind of real world calculations requires you to have more than 16 significant digits?

BTW, you may be able to use symbolics in a program too (at least you can copy a symbolic eval in a program in MC15). Furthermore you can evalaute your programm symbolically which may give you the accuracy you'd like to have.

1.png

Z
zhulaojianke1-VisitorAuthor
1-Visitor
August 27, 2014

I want to create a program that could translate arbitrary decimal to fraction. When the significant figure of the decimal less or equal than 16, my program work well, but when it large than 16, it will return a wrong result.

2014-08-27_233601.jpg

Eh, this program can't use x-trunc(x) to get the decimal part of the number, and I have try 20.12355, and when use x-trunc(x), the decimal part has been returned 0.123550000000016. So I translate it to string and process it.

But, Just like you have seen, when the significant figure of the number is large than 16, the result is wrong.

R
RichardJ19-Tanzanite
19-Tanzanite
August 27, 2014

That's the limit of the precision of double precision floating point numbers, which is what Mathcad uses for all numerical calculations. You have 16 significant digits.

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