tl;dr!? If $1 bought 1 inch, literally how much distance you could buy with increasing orders of magnitude?
Note: This information originally appeared in “Can we finally agree that trickle down doesn’t?” I have expanded the original text to include:
- scientific notation
- individuals or classes of people as markers of attainment
- a trillion inches or dollars and the national debt
The section ‘Background’ below contains the definitions, measurements, and conversion factors used to develop the following comparisons.
Dollars to Distance
How far does that dollar go if one dollar buys one inch? Shouting distance? Out of sight? Out of the country? Off the planet?
Here is the distance money buys you as represented as a distance at each increasing order of magnitude:
$1 = 1“
1 X 10**0 (“ten raised to the power of zero”)
One dollar is one inch which looks like large print taking up two lines of half-inch blue-lined paper. You sign your name with flourish. Or maybe it looks like a straight pin.
$10 = 10“
1 X 10**1 (“ten raised to the power of one”)
Ten dollars looks like 10” which is almost a foot. Ten inches looks like shoe. A bigger shoe, but a shoe.
$100 = 100“
1 X 10**2 (“ten raised to the power of two”)
One hundred inches is 8.33 ft. A standard ceiling height is 8 feet or about one hundred dollars in height.
$1000 = 1000“
1 X 10**3 (“ten raised to the power of three” or 1K)
One thousand inches is 83.33 feet which is 27.778 yards which if you’re a football team moving the ball from the 20 yard line is just 2.222 yards short of a first down (10 yards minus 7.778 yards).
$10,000 = 10,000“
1 X 10**4 (“ten raised to the power of four” or 10K)
Oh boy! Now we’re into using commas for readability. Ten thousand inches is 833.3 ft which is 277.78 yds which is 2.7778 football fields:
- Lambeau Field
- Aloha Stadium
- And 22.22 yds short of a touchdown at Soldier Field
The poverty line for a household of 1 person in 2019 is $12,490.
$100,000 = 100,000“
1 X 10**5 (“ten raised to the power of five” or 100K)
$1,000,000 = 1,000,000“
1 X 10**6 (“ten raised to the power of six,” “one million” or 1M)
One million inches is 15.78 miles which will take 15 minutes to drive at a speed of 63.12 MPH. I don’t have a great visual for ~ 16 miles. I did see this headline – “Most Americans think $1 million will be enough for a ‘comfortable retirement’ …” so maybe a smallish pot of gold?
** Reminder: we are working in units of dollars to INCHES. Inches convert to feet which convert to miles. Carry on. **
$10,000,000 = 10,000,000“
1 X 10**7 (“ten raised to the power of seven,” “ten million” or 10M)
Ten million inches is 157.83 miles which is a trip from Milwaukee to Chicago and 0.716 of the way back. Stop in Racine for dinner, whydoncha?
The adjacent apartments Jeff Bezos purchased in New York cost $80M or $8 X 10,000,000.
$100,000,000 = 100,000,000“
1 X 10**8 (“ten raised to the power of eight,” “one hundred million” or 100M)
One hundred million inches is 1,578.3 miles which is 4 miles short of a complete round trip from Milwaukee to Chicago to Washington DC and back. We are really moving now!
$100M is also the amount of money I heard Mitt Romney had in offshore accounts when he ran for President in 2012. Whatever the actual amount was, I believed such great holdings showed a serious love of money and lack of creativity for a Presidential candidate. I still do.
Jeff Bezos purchased a Los Angeles mansion for $165M.
$1,000,000,000 = 1,000,000,000“
1 X 10**9 (“ten raised to the power of nine,” “one billion” or 1B)
One billion inches is 15,783 miles which gets us international travel TO Hong Kong from Washington DC and 93% of the way back. And a billion dollars? If you have a billion dollars and lack imagination on what to do, here are my suggestions.
Forbes estimates the Green Bay Packers franchise value at $2.63B. Forbes so silly! Everyone knows the Packers are priceless.
$10,000,000,000 = 10,000,000,000“
1 X 10**10 (“ten raised to the power of ten,” “ten billion” or 10B)
Ten billion inches is 157,830 miles which is 6.338 trips around the earth at the equator.
- Jeff’s ex-wife, MacKenzie Bezos’ net worth is an estimated $42.2B.
- Michael Bloomberg’s net worth is an estimated $61.8B but his real worth is in his Twitter game.
Net worth source : Forbes.com, accessed February 13, 2020.
$100,000,000,000 = 100,000,000,000“
1 X 10**11 (“ten raised to the power of eleven,” “one hundred billion” or 100B)
One hundred billion inches is 1,578,300 miles which is out-of-this-world! It is 3 round trips from earth to moon and back with 144,900 miles still left over. Or, <does more math> almost 6 more trips around the earth (9,180,864,000 inches)!
- Jeff’s Bezos’ net worth is an estimated $130.7B.
- Jeff Bezos’ recent property acquisitions for $245M set him back 0.18 % of his net worth. Less than 1% of his worth for two residences.
- Bill Gates’ net worth is an estimated $112.9B.
- Bill Gates retired in 2014 at a net worth valued at $58B.
- If we consider that Bill has been retired for 10 years, 7 months, he has earned $174.09/second or the equivalent of 8.7 employees paid $20/hour.each.second .for. 10.yeARS. AND.7.MONTHS. EAT.THE.RICH. (Show your work: [$112,900,000,000-$58,000,000,000]/[10 years * 365 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute] = $174.09/second)
- Don’t get me wrong. Bill Gates and his heart may be in the right place. But his money, his philanthropy does not provide gainful employment for many people. Again, his net worth represents a lack of creativity and a systemic unregulated capitalism fail.
Source for net worths: Forbes.com, accessed February 13, 2020.
$1,000,000,000,000 = 1,000,000,000,000“
1 X 10**12 (“ten raised to the power of twelve,” “one trillion” or 1T)
One trillion inches is 15,783,000 miles which is out-of-this-world! It is 16.97% of a trip to the sun!
With the US National Debt in the $23 trillion dollar range we could travel in INCHES 3.9 times or almost 2 full round trips to the sun and back.
(Aside: I also explored the National Debt in this post: Scientific Notation.)
For those of you who want or need further documentation, these are the definitions, measurements, and conversion factors I used to develop the above information.
Definition by example: Base 10 Order of Magnitude
In base 10, the most common numeration scheme worldwide, an increase of one order of magnitude is the same as multiplying a quantity by 10. An increase of two orders of magnitude is the equivalent of multiplying by 100, or 102. In general, an increase of n orders of magnitude is the equivalent of multiplying a quantity by 10n.Margaret Rouse, WhatIs.com, accessed February 13, 2020
Scientific notation aids in accurately representing a very large or very small numbers from the reference point of the decimal point.
Scientific notation avoids inaccuracy in typing, reading, or counting the number of zeros to the right or left of the decimal point. By example:
- 10**n is “ten raised to the power of n”. The notation **n is useful when superscript is not immediately obvious or available.
- 1 X 10**13 or “ten raised to the power of 13” would be a 1 followed by 13 zeroes left of the decimal point, or 10,000,000,000,000.0
- 1 X 10**-9 or “ten to the negative ninth” would be a 1 preceded by 8 zeroes to the right of the decimal point, or 0.000000001
For this discussion, we will only concern ourselves with powers of ten to the left of the decimal point.
- 1 foot = 12 inches
- 1 yard = 3 feet
- 5,280 feet = 1 mile
In the event you want to check numbers used for imagery and illustration, these commonly recognized distances will be used for our Order of Magnitude math.
From the Googles:
- 100 yards = 1 football field
- The yard = 3 feet
- 5,280 feet = 1 mile
From the Googles:
- 100 yards = 1 football field
- The standard block size in Manhattan, NYNY is 264 ft by 900 ft. We’ll use the long side of the block – 900 ft.
- The distance from Milwaukee, WI to Chicago, IL is 92 mi.
- The distance from Chicago, IL to Washington DC is 699 mi.
- The distance from Washington DC to San Francisco, CA is 2,813 miles.
- The distance from Washington DC to Hong Kong is 8,140 miles.
- The circumference of the earth at the equator is 24,901 miles.
- The average distance from the earth to the moon is 238,900 miles.
- The average distance from the earth to the sun is 93,000,000 miles.
Thank you for taking this mental exercise with me! I find it helpful to take numbers which can sound so similar — millions and billions and trillions — and break them into relatable dimensions and discover they are really worlds apart or just out-of-this-world.
Any errors you find, I own. Peace.