Re: Scientific Format
Monnie Trbovich
Scientific notation 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.
I'm trying to process some data in Excel. The data includes numeric account numbers and other long numeric strings (like cell phone MEIDs). I am not doing math operations on these strings, so I want Excel to treat them as plain text.
The results remaining in scientific notation even though the cell is formatted as text just seems broken to me. I've seen suggested work-arounds like: use CSV import and set the format to text, add a space character to the beginning of each numeric string, and others.
Ah, memories of data munging back from when I did some massive number cross checking in Excel (never again).. When you punch in long numeric strings into Excel, try say, 12345678901234567890 (20 digits), Excel will generally convert it for you, meaning that the 20 digit number you've just tapped in has been cut back to be only about fifteen significant figures.
This occurs at point of entry, so once it's in, any additional detail is lost, and so even if you tell Excel that you really meant that was text, and not a number, you're kind of out of luck, and hence why your first sequence doesn't work.
A single apostrophe ' before a number will force Excel to treat a number as text (including a default left align). And if you have errors flagged, it will show as a number stored as text error on the cell.
I'm aware of the age of the question, but this is the one I've landed after google search and which did not answered my question (why formatting as text doesn't work and why number is cut down to 15 digits after format to text).
Short answer is: you can't work on your number the way you like AFTER you entered the numeric value and tapped Enter. The moment you do that the number will be truncated to 15 digits and presented in as exponential.
So what happens is that Excel autodetects type of input and if it's a number then it has precision limit of 15 digits and, if cell is formatted with 'General' format, it's displayed as exponential if value has 12 digits or more.
I believe it has to do with shell integration of Excel with '.CSV' files - in order for Excel to open them properly, assumptions have to be made. It is how Excel works for as long as I'm using it - that is: since 2001 at least.
Anything you do after that will be using the truncated value, so no formatting trick will help.However, you can use the Text to columns option to convert exponential notation to text (Click on column header, click Text to data, then Delimited, Next, untick all delimiter boxes, Select Text in Column data format and then Finish) to have the values converted to text and immediately displayed as 15 digit number. But, it will be only 15 digits, so if you had longer number, rest is "lost" to precision limit.
In order to have the number in the spreadsheet exactly the way you typed it in you have to store it as text. So you have two ways of doing that, but they will work only BEFORE/DURING editing:
If you're using method 1 and it "sometimes doesn't work", then, sorry, you either do something wrong or you have some sort of autocorrect on (if you use apostrophe and large number >15 digits Excel treats it as a wrong value and flags cell with warning message, so this remark is not personal nor critique).
Other way to do it in bulk numbers is to import values from text file. I dare say it's the only way for most situations. And be sure to import the file, not just open it, as Excel treats csv type like it's native format and trims large numbers to 15 digits as a matter of course.
Now, to the last issue. If you enter large numerical value in Excel cell formatted as text it will still be displayed in scientific notation as long as the cell is not wide enough. It's annoying, but side effect of some Excel internal algorithms. Just make the cell wider and you'll see full value every time.
Excel 2010: This works one column at a time and not at all for a row. Select the column or subset of a column, from the Data tab select "Text to Columns", and jump right to "Finish." No more scientific notation.
Excel is frustrating for CSV/bulk data work like this. Work with LibreOffice if possible, it doesn't do this, that is, if you open the same sheet (.xlsx) in Libreoffice, the large 'numbers' which are actually strings are not displayed in scientific notation (which is an absurd decision by Excel). LibreOffice's file fidelity is great: open the same .xlsx in Excel again, and the scientific notation instantly "works" just like usual.
The way I deal with this is I always first paste all the data into excel and note all the columns that have scientific notation. Then I undo the paste, highlight all the columns I noted before (Ctrl-Click) and change format to text. After that I re-paste and all the scientific notations disappear.
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