R Scientific Notation Off

[Sharon Harris]

Scientificnotation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations. On scientific calculators, it is usually known as "SCI" display mode.

or m times ten raised to the power of n, where n is an integer, and the coefficient m is a nonzero real number (usually between 1 and 10 in absolute value, and nearly always written as a terminating decimal). The integer n is called the exponent and the real number m is called the significand or mantissa.[1] The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the fractional part of the common logarithm. If the number is negative then a minus sign precedes m, as in ordinary decimal notation. In normalized notation, the exponent is chosen so that the absolute value (modulus) of the significand m is at least 1 but less than 10.

When a number is converted into normalized scientific notation, it is scaled down to a number between 1 and 10. All of the significant digits remain, but the placeholding zeroes are no longer required. Thus 1230400 would become 1.2304106 if it had five significant digits. If the number were known to six or seven significant figures, it would be shown as 1.23040106 or 1.230400106. Thus, an additional advantage of scientific notation is that the number of significant figures is unambiguous.

It is customary in scientific measurement to record all the definitely known digits from the measurement and to estimate at least one additional digit if there is any information at all available on its value. The resulting number contains more information than it would without the extra digit, which may be considered a significant digit because it conveys some information leading to greater precision in measurements and in aggregations of measurements (adding them or multiplying them together).

Some programming languages use other symbols. For instance, Simula uses & (or && for long), as in 6.022&23.[13] Mathematica supports the shorthand notation 6.022*^23 (reserving the letter E for the mathematical constant e).

In normalized scientific notation, in E notation, and in engineering notation, the space (which in typesetting may be represented by a normal width space or a thin space) that is allowed only before and after "" or in front of "E" is sometimes omitted, though it is less common to do so before the alphabetical character.[19]

Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation. None of these alter the actual number, only how it's expressed.

Conversion between different scientific notation representations of the same number with different exponential values is achieved by performing opposite operations of multiplication or division by a power of ten on the significand and an subtraction or addition of one on the exponent part. The decimal separator in the significand is shifted x places to the left (or right) and x is added to (or subtracted from) the exponent, as shown below.

For example, in base-2 scientific notation, the number 1001b in binary (=9d) is written as 1.001b 2d11b or 1.001b 10b11b using binary numbers (or shorter 1.001 1011 if binary context is obvious).[citation needed] In E notation, this is written as 1.001bE11b (or shorter: 1.001E11) with the letter "E" now standing for "times two (10b) to the power" here. In order to better distinguish this base-2 exponent from a base-10 exponent, a base-2 exponent is sometimes also indicated by using the letter "B" instead of "E",[26] a shorthand notation originally proposed by Bruce Alan Martin of Brookhaven National Laboratory in 1968,[27] as in 1.001bB11b (or shorter: 1.001B11). For comparison, the same number in decimal representation: 1.125 23 (using decimal representation), or 1.125B3 (still using decimal representation). Some calculators use a mixed representation for binary floating point numbers, where the exponent is displayed as decimal number even in binary mode, so the above becomes 1.001b 10b3d or shorter 1.001B3.[26]

Another similar convention to denote base-2 exponents is using a letter "P" (or "p", for "power"). In this notation the significand is always meant to be hexadecimal, whereas the exponent is always meant to be decimal.[29] This notation can be produced by implementations of the printf family of functions following the C99 specification and (Single Unix Specification) IEEE Std 1003.1 POSIX standard, when using the %a or %A conversion specifiers.[29][30][31] Starting with C++11, C++ I/O functions could parse and print the P notation as well. Meanwhile, the notation has been fully adopted by the language standard since C++17.[32] Apple's Swift supports it as well.[33] It is also required by the IEEE 754-2008 binary floating-point standard. Example: 1.3DEp42 represents 1.3DEh 242.

Convert a number to and from scientific notation, e notation, engineering notation, standard form, and real numbers. Enter a number or a decimal number or scientific notation and the calculator converts to scientific notation, e notation, engineering notation, standard form and word form formats.

Order of magnitude will also be identified for the calculated standard form. The order of magnitude when written in standard form, is the nth power of 10. For example, 3.4 x 10^5 has an order of magnitude of 5 since 10 is raised to the 5th power.

If you haave that many numbers to input, then you should type them into EXCEL. These can then be copied and pasted into Mathcad, or the EXCEL file can be read by Mathcad. (I prefer to have the numbers in the mathcad sheet, so copy and paste is my preferred way. Mathcad 14 and 15 will "Insert\Data\Table" and give you a table of blanks that you can then right-click and "paste table". Then you have a variable named array with the numbers right there. I tend to lose or break the links between an EXCEL file and the sheet. You can also read a CSV file, or even a binary file.)

For my money the ability to track units, the creation of a document that looks like a math sheet rather than a ledger or a computer program, the power of the program to manipulate information, and the solvers will keep me using Mathcad as long as I can.

From your questions/complaints it looks like you're just starting. Like any large, complex, capable piece of software there's a learning curve. It's not as steep with Mathcad as some I've climbed. QWTYRBTCHN

Since I've several times written million-line software packages with no such sloppiness, I have a higher standard than most users who have no programming experience and thus will serf-like endure whatever stupidities they encounter.

We have a basic difference in attitude (I think.) When you say, "programming," I think "FORTRAN," or "BASIC." I don't think of Mathcad as programming; to me it's a yellow quadrile pad that I use a pencil on. The advantage is that the pad auto-calculates, adjusts for units, and knows the numeric equivalent of pi, e, the gravity constant, g, and a whole bunch more. I haven't "programmed" in more than ten years.

Yes, Mathcad doesn't recognize 5E6 as a numeric value, probably because when you type 5 then E the editor/parser/interpreter assumes that you're going to multiply 5 times a variable (or unit) that begins with the letter E.

then shows x=0.051 as I expect. So why not be able to enter numbers that way? I DO see the convenience of assigning the value of e to the letter e, because in another package that I use I find it annoying that e is NOT the natural logarithm. For THAT e, I must use several keystrokes So if pasting works, why not keyboard entries?

I "program" quite a bit in other languages (such as MATLAB and Fortran) and I use the 5.1e-2 all the time...that's why I often make the mistake in Mathcad of entering the same thing, only to find that I get a result that I don't want. OTOH, I wish that I could use Mathcad for more of my work because I am so used to (well...almost addicted to) the visual whiteboard look.

while I agree with you that MathCad (MC 15 that is) has unique features such as unit conversion and solving I think that Bill has a point there. The previously simple and fast process of typing equations (for which one had to memorize only 7 keyboard shortcuts!) has now been rendered cumbersome by MathCad Prime. I'm not talking about having to get used to new shortcuts, but rather the tedious process where you frequently have to switch from keyboard to mouse and search for the proper icon. On top of that I'm finding the new cursor colour hard to see which simply adds to my annoyance.

Hmm, the main point of Bill's post 21 months ago was, that he accused the 10^x notation of being wasted keystrokes compared to the old Fortran notation. He counted 4 additional key strokes, in a later post he counted even 5. He counted the shift key as well but nevertheless in my count there are just three additional keystrokes necessary - I get the "^" without shift but have to use shift to get the "=", "(" and ")" - this may be different with other countries keyboard layouts.

As so far we now have (at least) 4 ways to type 5*10^20 using powers of ten. Comparing keystrokes, the standard way of doing is still the winner. Methods 3) and 4) additionally require the definition of e(x) and/or E(x) which leaves us w/o the Euler number :-(. Method 4) requires mouse action (I am not aware of a keyboard short for the selection of the prfix operator) and this sure would account for more than the two keystrokes I charged.

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