Is the maximum supported digits for a double type in c is 15 digits or more

Question

Is the maximum supported digits for a double type in c is 15 digits or more

Debojit Acharjee 455

I came to know from the Microsoft's site that a double variable in C can store a floating=point number up to 15 digits only, but in the following program I am able to store 17 digits. Why is that?

#include <stdio.h>

int main()
{
    double a;
    
    a = 12345678901234567;

    printf("%lf", a);

    return 0;
}

Output:

12345678901234568.000000

Ref: https://learn.microsoft.com/en-us/cpp/cpp/data-type-ranges?view=msvc-170

YujianYao-MSFT 4,296 Reputation points Microsoft External Staff

2023-06-02T08:25:49.2133333+00:00

Hi Debojit Acharjee,

May I know if you have got any chance to check my answer? If the reply is helpful, please click "Accept Answer" and kindly upvote it. It will also help others to solve the similar issue.

2 answers

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YujianYao-MSFT 4,296 Reputation points Microsoft External Staff

2023-06-02T08:25:49.2133333+00:00

Hi Debojit Acharjee,

May I know if you have got any chance to check my answer? If the reply is helpful, please click "Accept Answer" and kindly upvote it. It will also help others to solve the similar issue.

Answer 1

YujianYao-MSFT 4,296 Microsoft External Staff

Hi Debojit Acharjee,

The significand of the double type is approximately 15 to 17 decimal digits for most platforms. In most cases, a variable of type double can accurately represent 15 to 17 decimal digits. Numbers outside this range may lose precision or be rounded.

When I defined a 18 digits number, the result lost precision.

User's image

When using floating-point numbers, you should choose the appropriate data type according to your specific needs and precision requirements, and avoid using values beyond its representation range for calculations.

Regarding the double type, this documentation states:

Microsoft Specific The double type contains 64 bits: 1 for sign, 11 for the exponent, and 52 for the mantissa. Its range is +/-1.7E308 with at least 15 digits of precision.

You could also refer to this document for the float type.

Best regards,

Elya Yao

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didier bagarry 160 Reputation points

2023-05-29T09:12:17.6033333+00:00

The number 15, is what is guarantied for normal numbers.

E.g: 9999999999999997 lost its last digit (so only 15 valid digits), but 604462909807314587353088 keeps all its 23 digits!

Numbers are internally stored as powers of 2, because the last number is exactly 2pow79, it stays stored exactly.

Note that for very little numbers below DBL_MIN=2.2250738585072014e-308 (called denormal), the precision is less than 15 digits. e.g: 123456e-326 is kept as 123516e-326 with only 3 significant digits!
Debojit Acharjee 455 Reputation points

2023-06-02T13:15:45.7333333+00:00

but if a double type can store 15 digits then how come the number 12345678901234568.000000 is displayed?
YujianYao-MSFT 4,296 Reputation points Microsoft External Staff

2023-06-05T03:00:06.6033333+00:00

Hi Debojit Acharjee,

In C language, when you use the printf function and use %lf to output a variable of type double, it will display the value as a decimal.

Significant figures are the number of digits that can remain precise in a value, whether those digits are to the left or right of the decimal point.

In your code, the variable a is assigned the value 12345678901234567, which is a 17-bit number. Due to the precision limitation of double, it is difficult to accurately represent such a large number. Therefore, rounding or approximation occurs on output, causing the last digit to become 8 instead of the original 7.

Answer 2

Bruce (SqlWork.com) 77,686 Volunteer Moderator

A double is stored in base 2 not decimal. It’s stored in 64 bits. The mantissa is 52 bits, or max 179769313486232 in decimal. The exponent is 11 bits or max of 2047 in decimal. The final bit is the sign bit.

See:

https://en.wikipedia.org/wiki/Computer_number_format#:~:text=an%2011%2Dbit%20binary%20exponent,gives%20the%20actual%20signed%20value

Debojit Acharjee 455 Reputation points

2023-06-03T08:12:21.1966667+00:00

But you didn't answer my question--If on the Microsoft's site it's mentioned that a double can store 15 digits then why in my program the double type variable was able to store more?

https://learn.microsoft.com/en-us/cpp/cpp/data-type-ranges?view=msvc-170
Barry Schwarz 3,746 Reputation points

2023-06-03T19:43:00.8166667+00:00

It doesn't store more. It is just that some values can be represented exactly while other require rounding to the nearest representable value.
Debojit Acharjee 455 Reputation points

2023-06-04T13:30:44.8766667+00:00

How many digits are in this -> 12345678901234567? Is this 15 digits number? How come this is printed by a double variable?
Bruce (SqlWork.com) 77,686 Reputation points Volunteer Moderator

2023-06-04T16:45:45.2633333+00:00
To count the digits, you need to convert the decimal number to binary and then count. Let’s use unsigned char which has 8 bits.

unsigned char a = 1; // 00000001 1 digit unsigned char b = 10; // 00001010 4 digits unsigned char c = 255; // 11111111 8 digits unsigned char d = 256; // 00000000 0 digits (overflow)

So we say unsigned char can hold 2 digits, but sometimes 3. Now when you convert a binary floating point to decimal, you don’t get a perfect convert, it typically approximate.

for example 1/10 when converted to binary is a repeating number (similar to 1/3 in decimal)

.0001100110011001101…

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Is the maximum supported digits for a double type in c is 15 digits or more

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