I need some help in clearing up the difference between .9995 and
99.95%. First the background. Coin dealers on eBay and other auction
sites advertise US Mint Platinum Eagles (c) and Proofs as .9995. The
offical specs., from the US Mint.gov website states that ALL Platinum
bullion is 99.95% pure platinum. How did we "magicly" go from .9995,
which to me is 10,000 ths., to 99.95%? This is NOT jewelry, these are
platinum bullion coins issued by the US Mint and guaranteed for the
percentage of their pureness. I emailed one of the auction sellers,
and they are claiming that .9995 (no % sign,btw) is the SAME as
99.95%. If this is the case, why does the US Mint put the figure of
99.95% in ALL its' catalogs? Thankz to all the math persons out there.

Various web sites indicate that, in measuring the purity or fineness
of precious metals such as platinum, palladium, and gold -- both in
coins and in jewelry -- the decimal .9995 is the same as the
percentage 99.95%, or similarly, the decimal .9999 is the same as the
percentage 99.99%.

"Feature Article: Metals in Jewelry, Part 1: The 'K' in Gold"
All About Jewelry
http://www.2globalvillage.com/aaj/032001.htm

"Palladium: Prices"
United Nations Conference on Trade and Development (UNCTAD): Info Comm
http://www.unctad.org/infocomm/anglais/palladium/prices.htm

"Gold Depository: Precious Metals"
WHYY-TV12: Secrets Beneath the Streets
http://www.whyy.org/tv12/secrets/gold.html

None of these precious metals web sites actually explains why a
decimal like .9995 is the same as a percentage like 99.95%.  So I
searched for a good web site on mathematics.

A helpful web page from a Syracuse University web site explains that
"percent" means "per one hundred".  Thus, for example, 63% is the same
as the fraction 63/100, or in other words 0.63 (or just .63).  So, to
convert a percentage to a decimal, divide the percentage by 100.  
This is the same as moving the decimal point two places to the left. 
To convert the decimal back to a percent, you can multiply the decimal
by hundred, or move the decimal point two places to the right.

These rules work just as well for percentages or decimals with more
than two digits.  The web page has the example of the percentage 117%
and the decimal 1.17 -- to go from the percentage to the decimal,
divide by 100 or move the decimal point two places to the left, and to
go from the decimal to the percentage, multiply by 100 or move the
decimal point two places to the right.

"Review of Percents"
Center for Support of Teaching and Learning at Syracuse University:
Self-Instructional Mathematics Tutorials
http://cstl.syr.edu/fipse/Decunit/percent/percent.htm

These rules also solve the question you have asked.  If you divide
99.95 by 100 ("per cent") or move its decimal point two places to the
left, you get .9995.  And if you multiply .9995 by 100 or move its
decimal point two places to the right, you get 99.95%.

Or you can think of it this way.  If you have 99.95% of a dollar, that
would be 99.95 cents (hundredths of a dollar), which you could express
as the decimal $0.9995.

So likewise, if a coin contains 99.95% platinum, its platinum content
can be expressed as .9995.

I hope this answers your question to your satisfaction.  If not, I
will gladly provide a clarification.

- justaskscott-ga


Search terms used:

".9995" "99.95%"
".9999" "99.99%"
converting decimal percent

---

Request for Answer Clarification by stockzguy-ga on 22 Jun 2002 15:36 PDT

OK I have the basics, but you say that .9995 is represented and can be
converted to 100th of a dollar??? Wait a sec, according to my decimal
reference the .0000 is to the TEN THOUSANDTH place. How did we get
back to 100th of a dollar from ten thousandths? A penny is 1/100th of
a dollar 1/10000 of a dollar is what? Please clarify this.

---

Clarification of Answer by justaskscott-ga on 22 Jun 2002 17:10 PDT

I wasn't sure whether including the dollar example was useful or not,
and so perhaps I should have stopped the answer before that.  You can
ignore the dollar example if you'd like, and the answer might be more
clear without it.

However, I will elaborate on the dollar example, in case it's helpful.

99% of $1 is the same as 99 hundredths of a dollar, or $0.99.  OK, so
that explains how 99% is the same as 0.99.

If you increase the percentage from 99% to 99.95%, you would have 99
hundredths plus (here's the tricky part) 95 hundredths of a hundredth.

Another way of saying this is that you would have 99 hundredths plus
95 ten-thousandths.  (A hundredth of a hundredth is a ten-thousandth.)

That's how you get to the ten-thousandth place.  .99 (99 hundredths)
plus .0095 (95 ten-thousandths) equals .9995.

In other words, 99.95% of $1.00 is more than $0.99.  It is almost
$1.00, but not quite: it is $0.9995.

(In real life, of course, there is no coin called "a hundredth of a
cent".  For purposes of this example, you have to imagine that there
is.  Think of it this way: if you paid $99.95 for 100 items, the cost
of each item would be $0.9995, or 99 hundredths of a cent and 95
hundredths of a hundredth of a cent.)

I hope that this is helpful.

none

This is not a complicated math calculation. justaskscott-ga explained
it well, but I'll do so anyway.

one whole is 100%
1 = 100%
one half is 50%
0.5 = 50%

to convert decimal to percent, just multiply by 100, which is the same
thing as moving the decimal right two places.

0.75 = 75/100 = 75%

percentage, as stated, is just short for for "per one hundred."

Guys/gals I am emailing the question to my great friend and
mathmatician, Lenny. He may have a reason why they represent it as
.9995. Maybe the coin dealers think this is a "purer" metal
representation than 99.95%. As for me, I am staying with the US Mint'
99.95% figure, as that is a much easier symbol to convert than either
.9995 or .9999 contents. If any coin dealers or jewelry persons read
this, please add comments.

99.95%

= 99.95 / 100

= 999.5 / 1000

= 9995 / 10000

= 0.9995

...whether you use 0.9995 or 99.95% is purely a matter of personal
preference.

The average person on the street is going to be more familiar with
percentages.

Metallurgists (and scientists and engineers in general) probably find
factors more convenient to use.

If you know a coin is 0.9995 pure platinum, you can multiply its
weight directly by 0.9995 to get the amount of platinum in it.

But if you use percentages, then you must divide by 100 and later
multiply by 100 to get the same figure.

Really - the point is moot.

Mathematically, 99.95% is EXACTLY EQUAL to .9995.

The % percent sign (literally, per-cent - CENT is latin for 100) means
per-one hundred.  That is to say, out of 100 elements, 99.95 will
satisfy the prerequisite.

100 * 99.95% = 99.95.

If we think of 99.95% as 99.95 elements PER 100:
100 * 99.95/100 = 99.95.  (Duh.)

Thereby, if we use X to represent 99.95% as the variable X:
100 * X = 99.95.
X = 99.95/100
X = .9995

The difference between 99.95% and .9995 is MERELY SEMANTIC.  Nothing
more.

Ask any mathematician - when it boils down to numbers, they are
exactly the same.  Bar none.

Hope this clears up the issue.

OK everyone thankz for all the input/comments, I'll be over in the
corner banging my head against the monitor for a while :). No really,
we could go on for a long time over this, I get the point and I'd like
to give kudos to everyone who helped on this. I realize that decimals
absolutely need to be used in many cases, such as when using a gallon
of water' weight. And, of course, for tolerances, machining etc.

Gee, StockzGuy,
you really appear to be mixing up something here, but I have the
impression the basic problem is you don't see the difference between
absolute and relative measures.

Relative measures are indicated by a factor (e.g. one hundredth of
something, aka 1/100, 0.01 or 1%, that's just different notations). A
factor doesn't have any unit.

Absolute measures on the other hand, do have a unit (meter, gallon,
dollar, etc.)

Tolerances, for example, are usually indicated in absolute values, the
length of a mechanical part for example, could be 10 mm, +/- 0.1 mm.

The same tolerance, indicated as a factor, would be 0.01 (or 1%)
because 10 mm x 0.01 = 0.1 mm.

But if the part is, say, 20 mm, the same tolerance (+/- 0.1 mm) turns
out to be 0.02 (or 2%),...

.9995 * 100% = 99.95%  just consider the % sign as a coefficient