Maths question - Any brainboxes out there...?

[Rue]

I know GTP has many resident brain boxes so I thought you boffins would like a challenge, as any brain power I may have once had seems to have packed it's bags and moved on months ago. This morning I was stunned to see that the US National Debt has just hit $14.237 trillion. Quite a mind-boggling number and difficult to quantify. So my topical question is how far into space would a line of 14.237 trillion dollar bills reach if laid side by side?

Given that the dimensions of a US dollar bill are 6.6294cm (2.61in) wide, by 15.5956cm (6.14in) and the 14.237 trillion debt is 14,237,952,276,898 that would obviously make the simple sum of ...

15.5956*14,237,952,276,898

which equates to 2.22049409×1014

so, if the length in cm is 2.22049409×1014 I need to divide by 10,000 to get km which I'm looking for which is where I'm getting all unstuck.

Basically I'm looking for this answer 2.22049409×1014/10000 (Right?)

And if so, then what is that in millions, billions or trillions of km and what body in space would we be able to reach? Is the US National Debt to the moon, to Mars, the sun or further? I'm willing to bet it's not pretty.

 

[TB]

(14,237,952,276,898*(6.14/12))/5280 = 1,379,751,060 miles / 2,220,494,090km / 14.843 AU which according to this site would put it somewhere between Saturn and Uranus.

I think.

 

[Azuremen]

(14,237,952,276,898*(6.14/12))/5280 = 1,379,751,060 miles / 2,220,494,090km / 14.843 AU which according to this site would put it somewhere between Saturn and Uranus.

I think.

Looks all good to me. At least the setup. I really don't feel like dusting off my calculator.

Kind of crazy whenever you put things like this to distance.

 

[TB]

Looks all good to me. At least the setup.

Sweet.

Basically, Rue, the easiest way, at least in my mind, to crunch numbers like this is to get to the largest number needed as soon as possible:

(14,237,952,276,898*(6.14/12))/5280 = 1,379,751,060 miles
(National debt*(dollar in inches/12 inches gives you feet))/5280 feet gives you miles

From there, it's pretty simple, thanks to google.

 

[Barra333]

OK, since it appears TB is all over the original question like a rash, I will take this opportunity to ask:

What happens in ~6 weeks when the national debt reaches the 'debt limit' that the linked article in the OP states?

I have a science brain, not an economical/political one, so keep the answer as simple as possible

 

[Rue]

Great, thanks guys! That's scary indeed. Just over fifty-five thousand times around the Earth.

Thanks for the tip TB!

OK, since it appears TB is all over the original question like a rash, I will take this opportunity to ask:

What happens in ~6 weeks when the national debt reaches the 'debt limit' that the linked article in the OP states?

I have a science brain, not an economical/political one, so keep the answer as simple as possible

Quantitative Easing, Round 3 I imagine...

 

[Crash]

OK, since it appears TB is all over the original question like a rash, I will take this opportunity to ask:

What happens in ~6 weeks when the national debt reaches the 'debt limit' that the linked article in the OP states?

I have a science brain, not an economical/political one, so keep the answer as simple as possible

Quantitative Easing, Round 3 I imagine...

Well, what's likely going to happen is that Congress will debate legislation to raise the debt limit, then both parties will accuse each other of being completely fiscally irresponsible and is going to destroy America one way or another. After the finger-pointing is done, then likely a compromise will be reached raising the debt ceiling and allowing the government to continue selling bonds.

Typically, when the debt ceiling is reached, there are 2 options. One, Congress can pass legislation raising the debt ceiling, allowing us to borrow more, or two, the government will go into default. Rather than defaulting though, even if the debt ceiling isn't raised, there apparently are tricks that the Treasury department can use as stopgap measures. Ultimately, the debt ceiling will be raised, since I think Congressperson, even the most fiscally conservative ones, understands that letting the US default on its debt obligations will be... very very bad.

The whole QE2 thing isn't exactly the government debt. That's the Federal Reserve saying, "let's print more cash to increase the speed of cash circulation through the financial system!"

 

[Famine]

I know GTP has many resident brain boxes so I thought you boffins would like a challenge, as any brain power I may have once had seems to have packed it's bags and moved on months ago. This morning I was stunned to see that the US National Debt has just hit $14.237 trillion. Quite a mind-boggling number and difficult to quantify. So my topical question is how far into space would a line of 14.237 trillion dollar bills reach if laid side by side?

Given that the dimensions of a US dollar bill are 6.6294cm (2.61in) wide, by 15.5956cm (6.14in) and the 14.237 trillion debt is 14,237,952,276,898 that would obviously make the simple sum of ...

15.5956*14,237,952,276,898

which equates to 2.22049409×1014

so, if the length in cm is 2.22049409×1014 I need to divide by 10,000 to get km which I'm looking for which is where I'm getting all unstuck.

Basically I'm looking for this answer 2.22049409×1014/10000 (Right?)

And if so, then what is that in millions, billions or trillions of km and what body in space would we be able to reach? Is the US National Debt to the moon, to Mars, the sun or further? I'm willing to bet it's not pretty.

If you take a dollar bill to be 2.61" x 6.14", each one is 16 square inches - or roughly 0.11 square feet.

If there's 14,237,952,276,898 of them, you have 1,584,506,114,015 square feet - or 56,836 square miles - enough to paper over the entire of New York State with dollar bills (with enough left to paper over Hong Kong too).

 

[Rue]

If you take a dollar bill to be 2.61" x 6.14", each one is 16 square inches - or roughly 0.11 square feet.

If there's 14,237,952,276,898 of them, you have 1,584,506,114,015 square feet - or 56,836 square miles - enough to paper over the entire of New York State with dollar bills (with enough left to paper over Hong Kong too).

Good one Famine! Thought it wouldn't be long before you turned up. Or the whole of Iowa, Chicago or Wisonsin. Or if you want to go further afield, the US National Debt would cover Bangladesh with some dollars to spare.

 

[Touring Mars]

TB's answer is right, although your equation is wrong...

You said:

so, if the length in cm is 2.22049409×1014 I need to divide by 10,000 to get km which I'm looking for which is where I'm getting all unstuck.

Basically I'm looking for this answer 2.22049409×1014/10000 (Right?)

And if so, then what is that in millions, billions or trillions of km and what body in space would we be able to reach? Is the US National Debt to the moon, to Mars, the sun or further? I'm willing to bet it's not pretty.

To convert cm to km, you'd need to divide by 100000, not 10000 (there are 100 cm in 1 m, and 1000 m in 1 km, hence 100,000 cm in 1 km, not 10,000)

With that in mind:

100000 may be written as 105, so your equation becomes:

(2.2205×1014)/105, which itself can be written as 2.2205 x (1014/105)

Since 1014/105 = 109, and 109 = 1 billion, the answer is 2.2205 billion km.

 

[Eric.]

Good one Famine! Thought it wouldn't be long before you turned up. Or the whole of Iowa, Chicago or Wisonsin. Or if you want to go further afield, the US National Debt would cover Bangladesh with some dollars to spare.

I didn't realize Chicago was so big!

 

[DGiant2000]

Interesting problem, always good to see someone discussing Maths. TM is right though, there are 1,000,000mm in a km. Another interesting way to look at it is what if you stacked them one on top of the other?

Given the thickness of a dollar bill is 0.19022mm, it would reach a height of 14,237,952,276,898 x (1.0922 x 10-7) = 1,555,069.15km which is 175,753 times the height of everest!

This would take some shifting however as the weight of these dollar bills would be 14,237,952 tonnes (or 15,694,655 tons for you americans), or the weight of 123,101 jumbo jets!!

By the way, being British 14,237,952,276,898 should really be only 14 billion, some people do like to exaggerate

 

[Stevisiov]

By the way, being British 14,237,952,276,898 should really be only 14 billion, some people do like to exaggerate

The old British Billion is redundant these days.

 

[sumbrownkid]

Shouldn't you divide by 100,000 since there are 100 cm in a meter, and 1000 meters in kilometer. So 1000 x 100 = 100,000

why won't America just switch over to the metric system? It makes conversions so much easier.

 

[DK]

^ I don't think so, the likes of Fox News might consider the metric system as some sort of "liberal/Marxist/Chinese/Muslim conspiracy".

 

[Rue]

I didn't realize Chicago was so big!

I think I meant Illinois.

 

[PeterJB]

It seems slightly ridiculous that a group of notes that can fit into Illinois can extend out past Saturn, feels way to small a number of notse for that.

 

[Touring Mars]

It seems slightly ridiculous that a group of notes that can fit into Illinois can extend out past Saturn, feels way to small a number of notse for that.

Unless my back-of-fag-packet sums are wrong, you could actually fit all those dollar bills (all 14.238 trillion of them) into a cube 'just' 304 meters wide. For reference, that would be a box whose edges are as high/long as the Eiffel Tower.

 

[Famine]

Unless my back-of-fag-packet sums are wrong, you could actually fit all those dollar bills (all 14.238 trillion of them) into a cube 'just' 304 meters wide. For reference, that would be a box whose edges are as high/long as the Eiffel Tower.

I just checked and it'd be 1,001 feet across each side. Which is close enough.