# B Should We Think of .001 as 1%?

1. Aug 8, 2016

### kyphysics

I often get confused by conventions and meanings how we interpret decimals in relation to percent.

First, is 100% = 1 conventionally (or, logically)?

I ask, because I think I've seen people use .001 as meaning 1% and .1 as being 10%. But, that would mean 1 would be 100%.

Likewise, I seen people just use 100%, 10%, and 1%.

Does it really matter what we use, as long as one is consistent in the scale of things?

2. Aug 8, 2016

### Bandersnatch

1 per cent literally means 1 (part) in a hundred, in Latin.
0.01 (not 0.001!) means 1 hundredth - i.e. exactly the same thing. So it's no wonder these are used interchangeably.
100% is 100 parts in a hundred (100/100 = 1). 10% ten parts in a hundred (10/100 =0.1), and so on.

3. Aug 8, 2016

### symbolipoint

Percent, or using symbol, %, means "per onehundred parts".

100% means 1, according to the meaning described for "percent".

0.001 means 0.1% which means 0.1/100 which means 1/1000.

4. Aug 8, 2016

### Staff: Mentor

0.1 as 10% makes sense, but the first one is off by a factor of 10, as 1% is 0.01.

As long as it is consistent and clear, it does not matter.

5. Aug 8, 2016

### Staff: Mentor

I like to reduce the "fear" of percentage calculations by saying again and again:
Simply substitute $\%$ by $\cdot \frac{1}{100}$

(Opinion) I find the notation of "parts by" or "per parts" already misleading and unnecessary whereas the multiplication dot is essential.

6. Aug 8, 2016

### pwsnafu

Slightly off topic

0.001 is 1‰ (per mille). This is important because blood-alcohol is permille in Europe but percent in Australia, Canada and US, and permyriad (‱) in Great Britain (although IIRC they write as basis point "bp").

7. Sep 29, 2016

### Deepak suwalka

Whenever you get a number with a percent sign.
Then simply remove the percent sign and divide the number by 100.
a% = a/100
similarly,
1%=1/100 =0.01
10%=10/100 =0.1
100%=100/100 =1

8. Sep 29, 2016

### Staff: Mentor

Thread title: Should We Think of .001 as 1%?
No, for two reasons
1) A percentage represents a comparison to something; e.g., "My grade was 75% on that test." -- IOW, I received 75% or 3/4 of the points possible on that test. In a percentage, there's always some context about what constitutes all (or 100%) of whatever you're measuring/counting.
2) Converted to a decimal fraction, 1% is .01, not .001.

9. Oct 11, 2016

### bahamagreen

Thread title: Should We Think of .001 as 1%?

Depends on the answer to, "1% of what?" (that which Mark44 called context about what constitutes all)
Seems to me that percent is a transitive factor; it takes an object identifying that "of what?"
So... 1% is a factor of .01, but
1% of 300 is 3
5 is 1% of 500

And .001 is 1% of .1

10. Oct 11, 2016

### Staff: Mentor

Which makes it more comparative than transitive. I agree though that it needs to be understood what it is that we have some percentage of.
Not in the usual sense of the meaning of factor. We wouldn't normally write .01 = 1% x 1

11. Oct 15, 2016

### Learner60

Yes..you're talking the difference between thousands and hunred_ths...BIG difference!

12. Nov 1, 2016

### Prem1998

You are treating percentages like absolute numbers. Well, percentages were not invented for that but sometimes it's convenient. Percentages are more for comparisons. Think of the difference between decimals and fractions. Decimals are mostly absolute values. The quantity of something like its mass or volume can be a decimal depending on the unit. But, when are fractions more convenient?
The abundance of elements in earth's crust is usually expressed as a percentage. Let's suppose oxygen makes 20% by mass of earth's crust(I'm not saying it does). This means that the if the total mass of the crust is given the number 100, then the contribution of oxygen is 20. In fractions, it is 20/100. If we divide both by 10, the same fraction becomes 2/10. It's still a relative value. It just means that if crust is ten un mass, then oxygen is 2. Divide both by five and it becomes 4/20. Still it just mentions how much is oxygen relative to the crust. Finally, get rid of the denominater and we get 0.2. Now, is 0.2 the absolute contribution of oxygen by mass because we have only one number left? You're wrong because the number 1 is still hiding in the denominater. It just means that crust has been given the number 1.
But, sometimes, values are more absolute than relative. Let's just say that the mass of Earth is 0.01 Kg. Well, it's still a relative value because it just means thatif a standard object(it exists) has been the mass 1 kg, then our object under consideration is 1/100th of it's heavieness , so it must be given the number 0.01. But we don't say that the object is 1% of kg or 1% kg. We use 0.01 Kg because Kg is a frequently used unit to give relative heavieness to objects.