 Newcomposers.ru

IT Мир
0 просмотров
Рейтинг статьи      Загрузка...

# Too many decimal points in number

## Round a number to the decimal places I want

If you don’t want unnecessary decimal places in cells because they cause ###### symbols to appear, or you don’t need accuracy down to the microscopic level, change the cell format to get the number of decimal places you want.

Or if you want to round to the nearest major unit, such as thousands, hundreds, tens, or ones, use a function in a formula.

By using a button:

Select the cells that you want to format.

On the Home tab, click Increase Decimal or Decrease Decimal to show more or fewer digits after the decimal point.

By applying a built-in number format:

On the Home tab, in the Number group, click the arrow next to the list of number formats, and then click More Number Formats. In the Category list, depending on the type of data you have, click Currency, Accounting, Percentage, or Scientific.

In the Decimal places box, enter the number of decimal places that you want to display.

By using a function in a formula:

Round a number to the number of digits you want by using the ROUND function. This function has only two arguments (arguments are pieces of data the formula needs to run).

The first argument is the number you want to round, which can be a cell reference or a number.

The second argument is the number of digits you want to round the number to.

Suppose that cell A1 contains 823.7825. To round the number to the nearest:

Type =ROUND(A1,-3) which equals 1,00

823.7825 is closer to 1,000 than to 0 (0 is a multiple of 1,000 )

Use a negative number here because you want the rounding to happen to the left of the decimal point. The same thing applies to the next two formulas that round to hundreds and tens.

Type =ROUND(A1,-2) which equals 800

800 is closer to 823.7825 than to 900. We think you get the idea by now.

Type =ROUND(A1,-1) which equals 820

Type =ROUND(A1,0) which equals 824

Use a zero to round the number to the nearest single digit.

Type =ROUND(A1,1) which equals 823.8

Use a positive number here to round the number to the number of decimal points you specify. The same thing applies to the next two formulas that round to hundredths and thousandths.

Type =ROUND(A1,2) which equals 823.78

Type = ROUND(A1,3) which equals 823.783

Round a number up by using the ROUNDUP function. It works just the same as ROUND, except that it always rounds a number up. For example, if you want to round 3.2 up to zero decimal places:

=ROUNDUP(3.2,0) which equals 4

Round a number down by using the ROUNDDOWN function. It works just the same as ROUND, except that it always rounds a number down. For example, if you want to round down 3.14159 to three decimal places:

=ROUNDDOWN(3.14159,3) which equals 3.141

Tip: To get more examples, and to play around with sample data in an Excel Online workbook, see the ROUND, ROUNDUP, and ROUNDDOWN articles.

You can set a default decimal point for numbers in Excel Options.

Click Options (Excel 2010 to Excel 2016), or the Microsoft Office Button > Excel Options (Excel 2007).

In the Advanced category, under Editing options, select the Automatically insert a decimal point check box.

In the Places box, enter a positive number for digits to the right of the decimal point or a negative number for digits to the left of the decimal point.

Note: For example, if you enter 3 in the Places box and then type 2834 in a cell, the value will be 2.834. If you enter -3 in the Places box and then type 283 in a cell, the value will be 283000.

The Fixed decimal indicator appears in the status bar.

On the worksheet, click a cell, and then type the number that you want.

Note: The data that you typed before you selected the Fixed decimal check box is not affected.

To temporarily override the fixed decimal option, type a decimal point when you type the number.

To remove decimal points from numbers that you already entered with fixed decimals, do the following:

Click Options (Excel 2010 to Excel 2016), or the Microsoft Office Button > Excel Options (Excel 2007).

In the Advanced category, under Editing options, clear the Automatically insert a decimal point check box.

In an empty cell, type a number such as 10, 100, or 1,000, depending on the number of decimal places that you want to remove.

For example, type 100 in the cell if the numbers contain two decimal places and you want to convert them to whole numbers.

On the Home tab, in the Clipboard group, click Copy or press CTRL+C.

On the worksheet, select the cells that contain the numbers with decimal places that you want to change.

On the Home tab, in the Clipboard group, click the arrow below Paste, and then click Paste Special.

In the Paste Special dialog box, under Operation, click Multiply.

## Need more help?

You can always ask an expert in the Excel Tech Community, get support in the Answers community, or suggest a new feature or improvement on Excel User Voice.

## Numbers

In modern JavaScript, there are two types of numbers:

Regular numbers in JavaScript are stored in 64-bit format IEEE-754, also known as “double precision floating point numbers”. These are numbers that we’re using most of the time, and we’ll talk about them in this chapter.

BigInt numbers, to represent integers of arbitrary length. They are sometimes needed, because a regular number can’t exceed 2 53 or be less than -2 53 . As bigints are used in few special areas, we devote them a special chapter BigInt.

Читать еще:  Вк социальная сеть моя страница вход

So here we’ll talk about regular numbers. Let’s expand our knowledge of them.

## More ways to write a number

Imagine we need to write 1 billion. The obvious way is:

But in real life, we usually avoid writing a long string of zeroes as it’s easy to mistype. Also, we are lazy. We will usually write something like «1bn» for a billion or «7.3bn» for 7 billion 300 million. The same is true for most large numbers.

In JavaScript, we shorten a number by appending the letter «e» to the number and specifying the zeroes count:

In other words, «e» multiplies the number by 1 with the given zeroes count.

Now let’s write something very small. Say, 1 microsecond (one millionth of a second):

Just like before, using «e» can help. If we’d like to avoid writing the zeroes explicitly, we could say the same as:

If we count the zeroes in 0.000001 , there are 6 of them. So naturally it’s 1e-6 .

In other words, a negative number after «e» means a division by 1 with the given number of zeroes:

### Hex, binary and octal numbers

Hexadecimal numbers are widely used in JavaScript to represent colors, encode characters, and for many other things. So naturally, there exists a shorter way to write them: 0x and then the number.

Binary and octal numeral systems are rarely used, but also supported using the 0b and 0o prefixes:

There are only 3 numeral systems with such support. For other numeral systems, we should use the function parseInt (which we will see later in this chapter).

## toString(base)

The method num.toString(base) returns a string representation of num in the numeral system with the given base .

The base can vary from 2 to 36 . By default it’s 10 .

Common use cases for this are:

base=16 is used for hex colors, character encodings etc, digits can be 0..9 or A..F .

base=2 is mostly for debugging bitwise operations, digits can be 0 or 1 .

base=36 is the maximum, digits can be 0..9 or A..Z . The whole latin alphabet is used to represent a number. A funny, but useful case for 36 is when we need to turn a long numeric identifier into something shorter, for example to make a short url. Can simply represent it in the numeral system with base 36 :

Please note that two dots in 123456..toString(36) is not a typo. If we want to call a method directly on a number, like toString in the example above, then we need to place two dots .. after it.

If we placed a single dot: 123456.toString(36) , then there would be an error, because JavaScript syntax implies the decimal part after the first dot. And if we place one more dot, then JavaScript knows that the decimal part is empty and now goes the method.

Also could write (123456).toString(36) .

## Rounding

One of the most used operations when working with numbers is rounding.

There are several built-in functions for rounding:

Math.floor Rounds down: 3.1 becomes 3 , and -1.1 becomes -2 . Math.ceil Rounds up: 3.1 becomes 4 , and -1.1 becomes -1 . Math.round Rounds to the nearest integer: 3.1 becomes 3 , 3.6 becomes 4 and -1.1 becomes -1 . Math.trunc (not supported by Internet Explorer) Removes anything after the decimal point without rounding: 3.1 becomes 3 , -1.1 becomes -1 .

Here’s the table to summarize the differences between them:

These functions cover all of the possible ways to deal with the decimal part of a number. But what if we’d like to round the number to n-th digit after the decimal?

For instance, we have 1.2345 and want to round it to 2 digits, getting only 1.23 .

There are two ways to do so:

For example, to round the number to the 2nd digit after the decimal, we can multiply the number by 100 , call the rounding function and then divide it back.

The method toFixed(n) rounds the number to n digits after the point and returns a string representation of the result.

This rounds up or down to the nearest value, similar to Math.round :

Please note that result of toFixed is a string. If the decimal part is shorter than required, zeroes are appended to the end:

We can convert it to a number using the unary plus or a Number() call: +num.toFixed(5) .

## Imprecise calculations

Internally, a number is represented in 64-bit format IEEE-754, so there are exactly 64 bits to store a number: 52 of them are used to store the digits, 11 of them store the position of the decimal point (they are zero for integer numbers), and 1 bit is for the sign.

If a number is too big, it would overflow the 64-bit storage, potentially giving an infinity:

What may be a little less obvious, but happens quite often, is the loss of precision.

Consider this (falsy!) test:

That’s right, if we check whether the sum of 0.1 and 0.2 is 0.3 , we get false .

Strange! What is it then if not 0.3 ?

Ouch! There are more consequences than an incorrect comparison here. Imagine you’re making an e-shopping site and the visitor puts \$0.10 and \$0.20 goods into their cart. The order total will be \$0.30000000000000004 . That would surprise anyone.

But why does this happen?

A number is stored in memory in its binary form, a sequence of bits – ones and zeroes. But fractions like 0.1 , 0.2 that look simple in the decimal numeric system are actually unending fractions in their binary form.

In other words, what is 0.1 ? It is one divided by ten 1/10 , one-tenth. In decimal numeral system such numbers are easily representable. Compare it to one-third: 1/3 . It becomes an endless fraction 0.33333(3) .

So, division by powers 10 is guaranteed to work well in the decimal system, but division by 3 is not. For the same reason, in the binary numeral system, the division by powers of 2 is guaranteed to work, but 1/10 becomes an endless binary fraction.

Читать еще:  Из indesign в powerpoint

There’s just no way to store exactly 0.1 or exactly 0.2 using the binary system, just like there is no way to store one-third as a decimal fraction.

The numeric format IEEE-754 solves this by rounding to the nearest possible number. These rounding rules normally don’t allow us to see that “tiny precision loss”, but it exists.

## decimal point

1 decimal point

2 decimal point

3 decimal point

1. точка в десятичной дроби

4 decimal point

5 decimal point

6 decimal point

7 decimal point

8 decimal point

9 decimal point

10 decimal point

11 decimal point

12 decimal point

13 decimal point

14 decimal point

15 decimal point

16 decimal point

17 decimal point

18 decimal point

19 decimal point

20 decimal point

### См. также в других словарях:

Decimal point — Decimal Dec i*mal, a. [F. d[ e]cimal (cf. LL. decimalis), fr. L. decimus tenth, fr. decem ten. See , and cf. .] Of or pertaining to decimals; numbered or proceeding by tens; having a tenfold increase or decrease, each unit being ten… … The Collaborative International Dictionary of English

decimal point — decimal points N COUNT A decimal point is the dot in front of a decimal fraction … English dictionary

decimal point — ► NOUN ▪ a full point placed after the figure representing units in a decimal fraction … English terms dictionary

decimal point — n the ↑full stop in a decimal, used to separate whole numbers from ↑tenths, hundredths etc … Dictionary of contemporary English

decimal point — noun count the symbol . in a DECIMAL … Usage of the words and phrases in modern English

decimal point — noun the dot at the left of a decimal fraction • Syn: ↑percentage point, ↑point • Hypernyms: ↑mathematical notation * * * noun, pl ⋯ points [count] mathematics : the dot (as in .678 or 3.678) that separates a whole number from tenths, hundredths … Useful english dictionary

decimal point — UK / US noun [countable] Word forms decimal point : singular decimal point plural decimal points maths the symbol . in a decimal … English dictionary

decimal point — trupmenos skirtukas statusas T sritis informatika apibrėžtis Ženklas, skiriantis dešimtainės trupmenos trupmeninę dalį nuo sveikosios. Amerikiečiai šiam tikslui vartoja tašką, europiečiai, išskyrus anglus, kablelį. Lietuvoje trupmenos skirtukas… … Enciklopedinis kompiuterijos žodynas

decimal point — / desɪm(ə)l pɔɪnt/ noun a dot which indicates the division between the whole unit and its smaller parts (such as 4.75) COMMENT: The decimal point is used in the UK and USA. In most European countries a comma is used to indicate a decimal, so… … Dictionary of banking and finance

decimal point — noun a) A point (.) used to separate the fractional part of a decimal from the whole part. b) A decimal mark, any symbol used to separate the fractional part of a decimal from the whole part … Wiktionary

decimal point — noun Date: circa 1771 a period, centered dot, or in some countries a comma at the left of a proper decimal fraction (as .678) or between the parts of a mixed number (as 3.678) expressed by a whole number and a decimal fraction … New Collegiate Dictionary

## Decimal floating point number to binary

Create a program that takes a decimal floating point number and displays its binary representation and vice versa: takes a floating point binary number and outputs its decimal representation.

The output might be something like this:

## dc [ edit ]

Directly on the command line:

From the manpage: «To enter a negative number, begin the number with ‘_’. ‘-‘ cannot be used for this, as it is a binary operator for subtraction instead.»

## Fortran [ edit ]

This is a cut-back version of a free-format routine EATREAL that worked in a more general context. The text was to be found in an external variable ACARD(1:LC) with external fingers L1 and L2; L1 marked the start point and L2 advanced through the number. If a problem arose then an error message could denounce the offending text ACARD(L1:L2) as well as just say «Invalid input» or similar. The routine worked in base ten only, but it is a trivial matter to replace *10 by *BASE. Here however a possible base may extend beyond just the decimal digits, so it is no longer possible to rely on zero to nine only and their associated character codes, thus the «digit» is now identified by indexing into an array of digits, thereby enabling «A» to follow «9» without character code testing. As the INDEX function works with CHARACTER variables that are indexed from one, to get zero for the first character in DIGIT, one must be subtracted. For handling the rescaling needed for fractional digits, a table of powers of ten up to sixteen was defined, but now the base may not be ten so BASE**DD is computed on the fly. The original routine was intended for usages in the hundreds of millions of calls, so this version would be unsuitable! Further, the exponent addendum (as in 35E+16) can no longer be recognised because «E» is now a possible digit. In handling this, the exponent part was added to DD and who knows, the result may produce a zero DD as in «123.456E-3» but otherwise a MOD(DD,16) would select from the table of powers of ten, and beyond that would be handled by successive squaring. Few numbers are presented with more than sixteen fractional digits, but I have been supplied data supposedly on electric power consumption via the national grid with values such as 1.21282E-31 kilowatt-hours, and other values with twenty-eight digits of . precision?

Because on a binary computer most decimal fractions are recurring sequences of binary digits, it is better to divide by ten than to multiply by 0·1. Thus, although the successive fractional digits could be incorporated by something like P = P*BASE; X = X + D/P if the computer’s arithmetic was conducted in a base that is not compatible with BASE (for example, two and ten) each step would introduce another calculation error. It is better to risk one only, at the end.

Читать еще:  Appfabric sharepoint 2020

An alternative method is to present the text to the I/O system as with READ (ACARD,*) X , except that there is no facility for specifying any base other than ten. In a more general situation the text would first have to be scanned to span the number part, thus incurring double handling. The codes for hexadecimal, octal and binary formats do not read or write numbers in those bases, they show the bit pattern of the numerical storage format instead, and for floating-point numbers this is very different. Thus, Pi comes out as 100000000001001001000011111101101010100010001000010110100011000 in B64 format, not 11·0010010000111111011010101. Note the omitted high-order bit in the normalised binary floating-point format — a further complication.

The source is F77 style, except for the MODULE usage simply for some slight convenience in sharing DIGIT and not having to re-declare the type of EATNUM.

Rather than mess about with invocations, the test interprets the texts firstly as base ten sequences, then base two. It makes no complaint over encountering the likes of «666» when commanded to absorb according to base two. The placewise notation is straightforward: 666 = 6×2 2 + 6×2 1 + 6×2 0

Note again that a decimal value in binary is almost always a recurring sequence and that the exact decimal value of the actual binary sequence in the computer (of finite length) is not the same as the original decimal value. 23·34375 happens to be an exact decimal representation of a binary value whose digit count is less than that available to a double-precision floating-point variable. But although 1011·1101 has few digits, in decimal it converts to a recurring sequence in binary just as does 0·1.

## About the Decimal/Two’s Complement Converter

This is a decimal to two’s complement converter and a two’s complement to decimal converter. These converters do not complement their input; that is, they do not negate it. They just convert it to or from two’s complement form. For example, -7 converts to 11111001 (to 8 bits), which is -7 in two’s complement. (Complementing it would make it 7, or 00000111 to 8 bits.) Similarly, 0011 converts to 3, not -3.

## How to Use the Decimal/Two’s Complement Converter

### Decimal to Two’s Complement

• Enter a positive or negative integer.
• Set the number of bits for the two’s complement representation (if different than the default).
• Click ‘Convert’ to convert.
• Click ‘Clear’ to reset the form and start from scratch.

If you want to convert another number, just type over the original number and click ‘Convert’ — there is no need to click ‘Clear’ first.

If the number you enter is too big to be represented in the requested number of bits, you will get an error message telling you so (it will tell you how many bits you need).

### Two’s Complement to Decimal

• Enter a two’s complement number — a string of 0s and 1s.
• Set the number of bits to match the length of the input (if different than the default).
• Click ‘Convert’ to convert.
• Click ‘Clear’ to reset the form and start from scratch.

The output will be a positive or negative decimal number.

## Exploring Properties of Two’s Complement Conversion

The best way to explore two’s complement conversion is to start out with a small number of bits. For example, let’s start with 4 bits, which can represent 16 decimal numbers, the range -8 to 7. Here’s what the decimal to two’s complement converter returns for these 16 values:

Nonnegative integers always start with a ‘0’, and will have as many leading zeros as necessary to pad them out to the required number of bits. (If you strip the leading zeros, you’ll get the pure binary representation of the number.) Negative integers always start with a ‘1’.

If you run those two’s complement values through the two’s complement to decimal converter, you will confirm that the conversions are correct. Here is the same table, but listed in binary lexicographical order:

No matter how many bits you use in your two’s complement representation, -1 decimal is always a string of 1s in binary.

## Converting Two’s Complement Fixed-Point to Decimal

You can use the two’s complement to decimal converter to convert numbers that are in fixed-point two’s complement notation. For example, if you have 16-bit numbers in Q7.8 format, enter the two’s complement value, and then just divide the decimal answer by 2 8 . (Numbers in Q7.8 format range from -2 15 /2 8 = -128 to (2 15 -1)/2 8 = 127.99609375.) Here are some examples:

• 0101111101010101 converts to 24405, and 24405/2 8 = 95.33203125
• 1101010101110111 converts to -10889, and -10889/2 8 = -42.53515625

## Implementation

This converter is implemented in arbitrary-precision decimal arithmetic. Instead of operating on the binary representation of the inputs — in the usual “flip the bits and add 1” way — it does operations on the decimal representation of the inputs, adding or subtracting a power of two. Specifically, this is what’s done and when:

• Decimal to two’s complement
• Nonnegative input: Simply convert to binary and pad with leading 0s.
• Negative input (‘-’ sign): Add 2 numBits , then convert to binary.
• Two’s complement to decimal
• Nonnegative input (leading ‘0’ bit): Simply convert to decimal.
• Negative input (leading ‘1’ bit): Convert to decimal, getting a positive number, then subtract 2 numBits .

## Limits

For practical reasons, I’ve set an arbitrary limit of 512 bits on the inputs.  