# Estimation skills - Question 1

## How many Calories in a Cubic Light Year of Ice cream?

• ### way more than 10^100

• Total voters
18
• Poll closed .

#### boatsman

Joined Jan 17, 2008
186
Is that made by Tom and Jerry?

#### WBahn

Joined Mar 31, 2012
28,489
I wonder if any new engineers know how to use a slide rule??? That's all we had, oh, and a pencil (not a Biro) and paper!
Damn few -- almost entirely just those few that are actually interested in learning the fundamentals. Most of today's students have been indoctrinated in the mentality that learning how to do anything themselves that a calculator or Google could cough up answers for them is a total waste of their time and effort. They firmly believe that doing so is nothing but useless memorization.

In my high school, the class before me (Class of '82) was the last class to use slide rules in math classes. My class and one or two classes after me didn't use calculators and we still used the trig and log tables. But starting with the class after that the students had used calculators from early elementary school and couldn't grasp how to use the tables (because they couldn't grasp long multiplication or division and everything that goes along with it as far as really understanding a positional numbering system) so the school had to buy all new textbooks that didn't even have trig and log tables.

#### Hypatia's Protege

Joined Mar 1, 2015
3,226
Is that made by Tom and Jerry?
I'm uncertain -- But then congealed fat/sugar solutions (e.g. ice cream, eggnog batter, etc...) are all equal (equally revolting) to my delicate sensibilities

TTFN
HP

#### WBahn

Joined Mar 31, 2012
28,489
I'm uncertain -- But then congealed fat/sugar solutions (e.g. ice cream, eggnog batter, etc...) are all equal (equally revolting) to my delicate sensibilities

TTFN
HP
Revolting .... but damn tasty!

#### WBahn

Joined Mar 31, 2012
28,489
Hopefully this isn't too much of a spoiler, but it is estimated that there are about 10^80 to 10^85 fundamental particles in the known universe.

#### GopherT

Joined Nov 23, 2012
8,009

#### RichardO

Joined May 4, 2013
2,270
Hopefully this isn't too much of a spoiler, but it is estimated that there are about 10^80 to 10^85 fundamental particles in the known universe.
Ah, yes, but ice cream can have more calories than particles.

#### WBahn

Joined Mar 31, 2012
28,489
Ah, yes, but ice cream can have more calories than particles.
It sure seems that way -- especially the next morning!

#### Hypatia's Protege

Joined Mar 1, 2015
3,226
Hopefully this isn't too much of a spoiler, but it is estimated that there are about 10^80 to 10^85 fundamental particles in the known universe.
Like I said -- 10^100 is a HUGE value!

While I've resisted the temptation to represent 1 ly^3 in terms of familiar units of commerce, and, thus, apprise the accuracy of my guess -- I must confess that even the 'minimum option' (to wit: 10^50 Dietetic Cals) seems rather high...

Awaiting the 28'th with bated breath
HP

#### WBahn

Joined Mar 31, 2012
28,489
If you tried to eat that much you would be dead. So it is a negative number.
I can think of quite a few people who, were they to taste such a sweet demise, it would be a decidedly positive number.

#### GopherT

Joined Nov 23, 2012
8,009
@Hypatia's Protege wait no longer, because I cannot.

First, recreating my estimate attempt and estimate and then actual numbers.

So, my Mr. Estimator hat on...
I start with something I remember from high school days - Speed of light is 3 x 10^8 m/s (that's 286,282 miles/second for you non SI unit types)

- need to convert from meters/second to decimeters of light travel in a year.

3 x 10^8 m/sec = speed of light
x 10 dm/m (a cubic decimeter is a liter which is easily converted to a kilogram later).
================
3 x 10^9 dm/sec

x 3600 sec/hr
=============
1 x 10^13 dm/hr

x 24 hr/day
=========
3 x 10^14 dm/day ((((( Here I was already able to make my guess on 10^50 because we were not going to get close to 10^75 and running out of my 30 seconds of thinking time, then I continued to see how close I could get))))

x 365 days/year (round off 3 x 365.25 = 10^3)
==============
1 x 10^17 dm/year (distance in decimeters that light travels in a year)

cube to get volume, that is, multiply exponent by three, (17 x 3 = 51)
1 x 10^51 liters

density of ice cream = 1.1 kg/liter

1 x 10^51 (liter to kg conversion is not significant)

2000 Calories / kg - (I remembered hearing ice cream was 2 calories per gram)
================
2 x 10^54
================
I repeated this effort while driving and explaining to my passenger and ended up with 10^48. I was off by a factor of "a lot" (two million) but the options differ by "a lot a lot". These are very big numbers and very big differences between 10^50 and 10^75. Very big does not mean 25% or 33% difference, it means a whole lot of difference!

==================
==================
==================

Now, with exact numbers...
==================

Starting from miles/second because I memorized that to more significant digits than all other units an I am too lazy to look any thing up for this...

186282 miles/second
x 5280 feet/mile
x 12 inches/foot
x 2.54 cm/inch
x 0.1 dm/cm
===========
2.99792 x10^9 dm/second

x 3600 sec/hr
x 24 hr/day
x 365.25 days/year
===========
9.46071 x 10^16 dm/year

The sides of our cube are 9.46071 x 10^16 dm
Cube this number to get liters.

8.46781 x 10^50 liters in one cubic light year

convert to kg, multiply by 1.1 kg/liter

9.31458 x 10^50 kg ice cream

at 2070 Calories (kcal) / kg (per Wikipedia)

=====================
1.92812 x 10^54 Calories / cubic light year
=====================

Error from estimating = 4% (I was surprised and very lucky)

NOTE1: Notification of any errors is appreciated. Nit-pickiness about significant digits is not.
NOTE2: I realize the correct answer was not given as an option.
NOTE3: If I had to select an answer in the closing seconds of a multiple choice test, I would have picked "way more than 10^100" but 30 seconds of effort and I felt reasonably safe that I had the right answer (10^50).

Last edited:

#### boatsman

Joined Jan 17, 2008
186
@recklessrog said:
I wonder if any new engineers know how to use a slide rule??? That's all we had, oh, and a pencil (not a Biro) and paper!
Graffiti outside a technical school in UK: Before I came here I didn't know what an engineer was; now I is one.

#### WBahn

Joined Mar 31, 2012
28,489
Here was my chain of reasoning.

A light year is 3E8 m/s.
I know that a million seconds is about eleven days and so thirty of those is 330 days or about one year.
So 1 year is about 30E6 seconds. Multiplying them together (and noting that 900 ~= 1000) I have
1 ly ~= 1E16 meters.
Cube that and we have
1 ly^3 ~= 1E48 m^3 (at this point I knew which answer I was going to pick)
There's about 3 feet in a meter, so a cubic meter is about 30 cubic feet.
1 ly^3 ~= 3E49 m^3
There's about 7.5 gallons in a cubic foot and 7 * 3 is about 20, so
1 ly^3 ~= 2E50 gallons
There are 16 cups in a gallon, so
1 ly^3 ~= 3E51 cups
I figured that a cup of ice cream probably has about the same number of Calories as a candy bar, which is about 250 so I called it 200 Calories/cup.
1 ly^3 ~= 6E53 cups

A number of my estimates were on the low side, so I rounded up to 10^54 Calories/ly^3.

At least I think that's the number I came up with -- I just did it from scratch here.

#### #12

Joined Nov 30, 2010
18,224
Awaiting the 28'th with bated breath
Another vocabulary lesson.
The first time I heard that phrase it was Tom (the cat) trying to catch Jerry (the mouse) with (cartoon) cheese on his tongue.
The cat was waiting for the mouse with baited breath.
Now I see it in print and assume the origin is, "abated".

This is the same kind of phonetic misinterpretation that has today's Facebook members saying, "Someone should of" done something.
They don't know, "should've" is a contraction because they can't spell in the first place.

Sorry for the hijack, but this has been a public service announcement.

#### GopherT

Joined Nov 23, 2012
8,009
Sorry for the hijack, but this has been a public service announcement.
I expected a PSA topic to align with one of your specialties. Let's see if anyone calls you for the cross-over into HP's work space.

#### #12

Joined Nov 30, 2010
18,224
I expected a PSA topic to align with one of your specialties. Let's see if anyone calls you for the cross-over into HP's work space.
HP doesn't explain herself unless you call her out...so I did.
I expect to see a treatise on the difference between, "bated" and "abated" any minute now.

#### Hypatia's Protege

Joined Mar 1, 2015
3,226
Now I see it in print and assume the origin is, "abated".
I've not explored the etymology, howbeit such was/is my assumption also -- Seems "Shakespearean leanings" will out

I expect to see a treatise on the difference between, "bated" and "abated" any minute now.
Off hand, it seems (as regards modern usage) that "abate" is well nigh synonymous with "ameliorate" -- I can but guess that 'abate' was formally applicable to moderation in general (as opposed to its current restricted sense of 'moderation of adversity') -- But hey! These are merely 'lexical musings' to be 'taken' at the reader's peril

"Someone should of"
To be filed alongside: "for all intensive purposes", "At your beacon call", "For crime out loud", "You've got another thing coming" and, most egregiously, confusion of "sufferance" and "suffrage"

Then there's a certain party near and dear to my heart who defiles the pristine sanctity of SMS-Speak Via abbreviation of "Because" with "cuz" on the grounds that "cos" might be confused with the cosine function -- But for the economy of a few characters, the 'rising generations' might have attained literacy

Sprinting for fallout shelter
HP

#### Hypatia's Protege

Joined Mar 1, 2015
3,226
@Hypatia's Protege wait no longer, because I cannot.

First, recreating my estimate attempt and estimate and then actual numbers.

So, my Mr. Estimator hat on...
I start with something I remember from high school days - Speed of light is 3 x 10^8 m/s (that's 286,282 miles/second for you non SI unit types)

- need to convert from meters/second to decimeters of light travel in a year.

3 x 10^8 m/sec = speed of light
x 10 dm/m (a cubic decimeter is a liter which is easily converted to a kilogram later).
================
3 x 10^9 dm/sec

x 3600 sec/hr
=============
1 x 10^13 dm/hr

x 24 hr/day
=========
3 x 10^14 dm/day ((((( Here I was already able to make my guess on 10^50 because we were not going to get close to 10^75 and running out of my 30 seconds of thinking time, then I continued to see how close I could get))))

x 365 days/year (round off 3 x 365.25 = 10^3)
==============
1 x 10^17 dm/year (distance in decimeters that light travels in a year)

cube to get volume, that is, multiply exponent by three, (17 x 3 = 51)
1 x 10^51 liters

density of ice cream = 1.1 kg/liter

1 x 10^51 (liter to kg conversion is not significant)

2000 Calories / kg - (I remembered hearing ice cream was 2 calories per gram)
================
2 x 10^54
================
I repeated this effort while driving and explaining to my passenger and ended up with 10^48. I was off by a factor of "a lot" (two million) but the options differ by "a lot a lot". These are very big numbers and very big differences between 10^50 and 10^75. Very big does not mean 25% or 33% difference, it means a whole lot of difference!

==================
==================
==================

Now, with exact numbers...
==================

Starting from miles/second because I memorized that to more significant digits than all other units an I am too lazy to look any thing up for this...

186282 miles/second
x 5280 feet/mile
x 12 inches/foot
x 2.54 cm/inch
x 0.1 dm/cm
===========
2.99792 x10^9 dm/second

x 3600 sec/hr
x 24 hr/day
x 365.25 days/year
===========
9.46071 x 10^16 dm/year

The sides of our cube are 9.46071 x 10^16 dm
Cube this number to get liters.

8.46781 x 10^50 liters in one cubic light year

convert to kg, multiply by 1.1 kg/liter

9.31458 x 10^50 kg ice cream

at 2070 Calories (kcal) / kg (per Wikipedia)

=====================
1.92812 x 10^54 Calories / cubic light year
=====================

Error from estimating = 4% (I was surprised and very lucky)

NOTE1: Notification of any errors is appreciated. Nit-pickiness about significant digits is not.
NOTE2: I realize the correct answer was not given as an option.
NOTE3: If I had to select an answer in the closing seconds of a multiple choice test, I would have picked "way more than 10^100" but 30 seconds of effort and I felt reasonably safe that I had the right answer (10^50).

Without wishing to appear a 'spoilsport'; -- I thought the idea was to make an intuitive guess? --- Anyone can calculate it! Why are you 'cheating' your own exercise?!?!?! -- Oh well! - It's your thread after all -- and then there is the 'balm' of my guess being "correct" --- So... that'll have to qualify as a 'good go'

Very best regards
HP