### Apple's amusingly round reuse figures

If you take a look at Apple's Environment page you might well be impressed by the amount of reuse Apple is getting by taking back devices. The numbers look great:

What's weird about these numbers is that they are round numbers. In fact they are very simple, round numbers. You just have to be using the right units.

Just look at that... 2,204 lbs of gold.

But wait! Isn't 1kg roughly 2.204 lbs? (Why, yes. It's 2.20462 lbs). So, sounds like Apple recovered 1,000 kg of gold. Now take a look at tin... 4,408 lbs... 2,000 kg. And silver... 6,612 lbs... 3,000 kg. And lead... 44,080 lbs... 20,000 kg.

Here are the figures above converted to kg using 1 kg = 2.204 lbs.

```Steel    28,101,000 lbs = 12,750,000 kg
Plastics 13,422,360 lbs = 6,090,000 kg
Glass    11,945,680 lbs = 5,420,000 kg
Aluminum  4,518,200 lbs = 2,050,000 kg
Copper    2,953,360 lbs = 1,340,000 kg
Cobalt      189,544 lbs = 86,000 kg
Zinc        130,036 lbs = 59,000 kg
Lead         44,080 lbs = 20,000 kg
Nickel       39,672 lbs = 18,000 kg
Silver        6,612 lbs = 3,000 kg
Tin           4,408 lbs = 2,000 kg
Gold          2,204 lbs = 1,000 kg
```

Every single number given by Apple is an exact number of metrics tons (tonnes).

It's doubtful that Apple obtained precisely 1,000 kg of gold or 86,000 kg of cobalt. My guess is someone in Apple came up with rounded figures and they got converted to lbs for public consumption.

In the process they ended up looking precise.

One mystery remains. The total recovered is 27,839,000 kg which is 61,357,156 lbs (using 1kg == 2.204 lbs). But Apple reports an extra 644 lbs (total 61,357,800 lbs). I'll send a copy of my book, The Geek Atlas, to the first person to send me a convincing argument where those 644 lbs came from.

PS This comment points out that the UK Apple site gives the figures in tonnes.

PPS Another comment points out that the Australian Apple site appears to have converted back from lbs to kg.

PPPS Khalil Kacem (and below) has a convincing answer to the 644 lbs question. He gets the book.

Mark L said…
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Unknown said…
They used more precise conversion for calculations and then rounded it to 1lbs for display.
tacos said…
"911 Metallurgist, which helps mines and recyclers extract precious metals from ore and, apparently, phones, has exhaustively checked the iPhones and other mobile devices. Each iPhone 5, for instance, contains \$1.58 of gold, \$.36 of silver, \$.05 of platinum, and \$.12 of copper."

So I'll say the missing item is platinum.
Lex Lexical said…
I can suggest an answer for the remaining 644lbs: rounding errors

Here's my hypothesis:

1. The figures were measured with reasonable accuracy on a per-material basis.
2. The per-material measurements were taken in kg. That's an ISO standard unit, and the initiatives are global after all.
3. The accurate measurements for 12 materials were then summed to produce the grand total that was probably a bit less than 27,839,000kg.
4. Next, all the figures were rounded to the nearest 1,000kg. Because hey, iProducts have round edges.
5. Some precision was lost in the process for each measurement. Across a large set, we can expect the errors to average out – but here our set is only N=12, so not huge. So, more of the numbers were reduced than increased; but the grand total number happened to be increased in the rounding.

Sanity check: the discrepancy is about 292kg, or ~25kg for each measurement. That's a couple of orders of magnitude lower than the rounding margin (nearest 1000).

T
This comment has been removed by the author.
JMart said…
Maybe they threw in the scraps from the manufacturing process. They realized they actually had a little more on hand that was "salvageable" and over 600 lb moves the needle enough to be worth adding to the number?
Aren Cambre said…
My guess: one or a few of the metric figures had more degrees of precision, and the total incorporated those numbers and then rounded, instead of just adding up the rounded ones. I've seen this in scientific calculations.
Luc said…
I don't know. The closest I can get if by summing ceil(pounds / 1000, 1 sf), which gets me to 61.357.700.
Dave said…
I suggest it's the rounded totals of various other precious elements.
For example, there's no mention of Indium which is supposedly rare and expensive, so we'd have to assume they did recover it. http://link.springer.com/article/10.1007%2Fs11661-009-9786-4#/page-1 gives a method for recovery and a figure of 6.2mg indium/phone.
http://money.cnn.com/2011/10/13/technology/iphone_trade_in/ gives a figure of 34mg of gold/phone; so taking the 2204lbs of gold as the start,

6.2*2204
-------- = 402lb
34

(Or 1000kg->182kg which you round to 200kg and call 440lb)

My bet is that the Indium end up rounded to 300kg which ends up as 661kg which gets to within the rounding to 100lb that your total has.
Unknown said…
They simply rounded the weights in pounds to next hundred which resulted in the extra 644lbs.

Python code:

import math
def roundup(x):
return int(math.ceil(x / 100.0)) * 100

materials_in_kgs = [12750000,6090000,5420000,2050000,1340000,86000,18000,20000,59000,2000,3000,1000]

materials_in_lbs = [i*2.204 for i in materials_in_kgs]

materials_in_lbs_rounded = [roundup(i) for i in materials_in_lbs]

print sum(materials_in_lbs_rounded)
Unknown said…
This comment has been removed by the author.
Unknown said…
This comment has been removed by the author.
Unknown said…
The logistics company who operates this waste would have supplied these figures, there's no conspiracy at work here.

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