How do you write these numbers from least to greatest: 0.63, 0.6, 0.633, 0.603, 0.06?

1. Numbers 6.0
2. Vcenter Build Numbers 6.0

2 Answers

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Explanation:

Lets write fully every number:

#0.06=0.06000#
#0.6=0.6000#
#0.603=0.6030#
#0.63=0.6300#
#0.633=0.6330#

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It's like thousands, only in decimal places, if that makes sense to you.

So there you go:

#0.06<0.6<0.603<0.63<0.633#

Explanation:

Write them with the same number of decimal places as this makes them easier to compare.

Then write them underneath each other with the decimal points aligned. Then compare the place holders, working from left to right to identify the biggest and smallest numbers,

#0.630#
#0.600#
#0.633#
#0.603#
#0color(blue)(.0)60' 'larr# this is the smallest. There are #0/10#

All the others have at least #6/10' '(0.6)#

Consider the second decimal places (hundredths)

#0.6color(red)(3)0' 'larr# bigger
#0.6color(red)(0)0' 'larr# smaller
#0.6color(red)(3)3' 'larr# bigger ##0.6color(red)(0)3' 'larr# smaller

Re-arrange them:

#0.6color(red)(0)0' 'larr# smaller
#0.6color(red)(0)3' 'larr# smaller

#0.6color(red)(3)0' 'larr# bigger
#0.6color(red)(3)3' 'larr# bigger

Now compare the third decimal places:

#0.60color(limegreen)(0)' 'larr# smaller
#0.60color(limegreen)(3)' 'larr# bigger

#0.63color(red)(0)' 'larr# smaller
#0.63color(red)(3)' 'larr# biggest of them all

The order from smallest to biggest is:

#0.06' '0.6' '0.603' '0.63' '0.633#

Related questions

The GMP computers are maintained by a single person on a volunteer basis. Theongoing Intel CPU bug debacle withMeltdown,Spectre,Foreshadow,MDS,the jCC/cache-line bug, Fallout, LVI, Portsmash, etc, etc, and theMEbackdoor is making the main GMP server far from as secure as we'd like it to be.

The system which runs this web server as well as mail server, mailing listserver, firewall, etc, has an Intel E5-1650 v2 which is affected by most of thebugs/backdoors mentioned above. Please keep that in mind when using theresources here.

Please understand that we don't take security lightly, but that we effectivelyareDoS'ed bysloppy/malicious engineering.

Thanks to a very generous donation from Christian Calderon, the GMP project nowhas a brand new, AMD Epyc server which will replace the old server. This isgreat for GMP, not only because of the old server's hardware security issues,but also since the new server is 3x more powerful than the old one.

The new server will be replacing the old server as soon as we have had time toinstall all subsystems, which we expect will happen by mid April.

Here are the specs of the system Christian has given us:

• Supermicro barebone 1114S-WTRT
• AMD Epyc 7402P 24-core CPU
• 256 GiB of ECC RAM
• 1.6 TB PCIe SSD disk (Samsung PM1735)

What is GMP?

GMP is a free library for arbitrary precision arithmetic, operating onsigned integers, rational numbers, and floating-point numbers. There is nopractical limit to the precision except the ones implied by the availablememory in the machine GMP runs on. GMP has a rich set of functions, and thefunctions have a regular interface.

The main target applications for GMP are cryptography applications andresearch, Internet security applications, algebra systems, computationalalgebra research, etc.

GMP is carefully designed to be as fast as possible, both for small operandsand for huge operands. The speed is achieved by using fullwords as the basicarithmetic type, by using fast algorithms, with highly optimised assembly codefor the most common inner loops for a lot of CPUs, and by a general emphasis onspeed.

The first GMP release was made in 1991. It is continually developed andmaintained, with a new release about once a year.

Since version 6, GMP is distributed under the dual licenses, GNU LGPL v3and GNU GPL v2.These licenses make the library free to use, share, and improve, and allow youto pass on the result. The GNU licenses give freedoms, but also set firmrestrictions on the use with non-free programs.

GMP is part of the GNU project. For more information about the GNU project,please see the official GNU web site.

GMP's main target platforms are Unix-type systems, such as GNU/Linux,Solaris, HP-UX, Mac OS X/Darwin, BSD, AIX, etc. It also is known to work onWindows in both 32-bit and 64-bit mode.

GMP is brought to you by a team listed inthe manual.

GMP is carefully developed and maintained, both technically and legally. Weof course inspect and test contributed code carefully, but equally importantlywe make sure we have the legal right to distribute the contributions, meaningusers can safely use GMP. To achieve this, we will ask contributors to signpaperwork where they allow us to distribute their work.

GMP function categories

There are several categories of functions in GMP:

1. High-level signed integer arithmetic functions (mpz). There are about 150 arithmetic and logic functions in this category.
2. High-level rational arithmetic functions (mpq). This category consists of about 35 functions, but all mpz functions can be used too, by applying them to the numerator and denominator separately.
3. High-level floating-point arithmetic functions (mpf). This is the GMP function category to use if the C type `double' doesn't give enough precision for an application. There are about 70 functions in this category. New projects should strongly consider using the much more complete GMP extension library mpfr instead of mpf.
4. C++ class based interface to all of the above. (The C functions and types can of course be used directly from C++ too.)
5. Low-level positive-integer, hard-to-use, very low overhead functions are found in the mpn category. No memory management is performed; the caller must ensure enough space is available for the results. The set of functions is not always regular, nor is the calling interface. These functions accept input arguments in the form of pairs consisting of a pointer to the least significant word, and an integral size telling how many limbs (= words) there are in that argument. The functions in the other categories call mpn for almost all their calculations. Of these functions about 60 are public.

Download the latest release of GMP

To try to verify that the file you have downloaded has not been tamperedwith, you can check that the GnuPG signature matches the contents of the file.Use yourGnuPG software or akey server directly to get the key that wasused for creating the signature. Starting from the repackaging of gmp-5.1.0 asgmp-5.1.0a.tar.* the following key is used to sign GMP releases:

Key ID: 0x28C67298
Key type: 2560 bit RSA
Fingerprint: 343C 2FF0 FBEE 5EC2 EDBE F399 F359 9FF8 28C6 7298


Instead of using a release, you may also get the latest code from theGMP repositories. This will require somemore work compared to using a release.

Reporting bugs in GMP

Please first see themanual on how to report bugs. Theproper address for bug reports is gmp-bugs at gmplib.org.

Most problems with GMP these days are due to problems not in GMP, but withthe compiler used for compiling the GMP sources. This is a major concern tothe GMP project, since an incorrect computation is an incorrect computation,whether caused by a GMP bug or a compiler bug. We fight this by making the GMPtestsuite have great coverage, so that it should catch every possiblemiscompilation.

GMP mailing lists

Note that we perform spam and virus filtering of these lists. The listshave been 100% spam-free during the last years.

We're blocking all mail from PR China, since 99% ofthe spam arriving to the GMP moderators emanates from PR China. If you areaffected but have a legitimate reason to send mail to the GMP project, e.g., ifyou work at a university or corporation with an interest in GMP, please let usknow; we will open access for you.

Status of the current release

The current stable release is 6.2.1, released 2020-11-14.

Issues with GMP 6.2.1:

• While we added support for Apple's new Arm based computers, our support has a problem. The problem is that Apple reserves CPU register x18, but GMP's mpn/arm64 assembly code uses that register. While GMP runs fine in our tests, we expect things to go awry in some execution situation. (Apple has not been kind enough to specify how they use x18. Therefore, we don't know what the consequences of using x18 might be.)

Issues with GMP 6.2.0:

• MacOS Xcode 11 prior to 11.3 miscompiles GMP, leading to crashes and miscomputation.

Issues with GMP 6.1.2:

• MacOS Xcode 11 prior to 11.3 miscompiles GMP, leading to crashes and miscomputation.

Issues with GMP 6.1.1:

• There are several issues with mini-gmp. Please see the special mini-gmp-status page.

Issues with GMP 6.1.0:

• An assembly file which is used for Intel Broadwell and Intel Skylake (except crippled Pentiums and Celerons without BMI2) will not work correctly for Windoze. Patch.
• See also issues for subsequent releases above.

Issues with GMP 6.0.0:

• [No issues found yet.]
• See also issues for subsequent releases above.

Issues with GMP 5.1.3:

• The documentation of mpn_set_str is incorrect and incomplete wrt allocation requirements. Patch.
• See also issues for subsequent releases above.

Issues with GMP 5.1.2:

• The functions mpn_sbpi1_div_qr_sec and mpn_sbpi1_div_r_sec compute incorrect results for some operands. With uniformly distributed random operands, the error is very hard to trigger, and for the intended use of these functions, operands can be expected to appear as such random operands from these functions' perspective. Patch.
• The internal function mpn_divrem_2 on Itanium clobbers two callee-saves registers. This can lead to miscomputations or crashes in the callers. Patch.
• See also issues for subsequent releases above.

Issues with GMP 5.1.1:

• Windows only: A 64-bit build for AMD Bulldozer and Piledriver chips, or a fat 64-bit build running on these chips, will not work correctly. Patch.
• The function mpz_powm_ui computes garbage if the base argument is over 15000 decimal or the mod argument is at least 7500 decimal digits. No other GMP powm function is affected. Patch.
• See also issues for subsequent releases above.

Issues with GMP 5.1.0:

• The mini-gmp.c file, which implements a subset of mpn and mpz, was not properly tested and contained a number of bugs. Please do not use the 5.1.0 version of mini-gmp.c. Note that these bugs do not affect GMP itself.
• The included top-level Makefile.in has an automake-generated distcheck target which creates a world-writable directory. This target is not used in the GMP release process, but it is a potential security problem affecting users who invoke this make target. This problem (and no other) is corrected in the gmp-5.1.0a.tar.* set of files.
• See also issues for subsequent releases above.

Numbers 6.0

For patches to older GMP versions, please see theInfo on older GMP releases.

Vcenter Build Numbers 6.0

Future releases

Please see the GMPng page for information onwhat we're working on.