Math Shortcuts - sense of scale part 4

For most of us (myself included), millions, billions and trillions are “big”. It’s not intuitively obvious that a trillion is actually a million squared — that is, a trillion makes 1 million look imperceptible.

Check out these:

• 1 second is 1 second
• 1 million seconds is 12 days (Interesting)
• 1 billion seconds is 30 years (Wow, that’s a lot)
• 1 trillion seconds is 30,000 years (Jumpin’ Jillikers!)

Yowza. Do you feel the staggering difference between a trillion and a million? Between a billion and a million?

And for distance:

• 1 millimiter is 1 mm (pretty tiny)
• 1 million mm is a kilometer (down the street)
• 1 billion mm is a 1000 km (600 miles — partway across the country)
• 1 trillion mm is 1,000,000 km (Going around the world 25 times, almost as wide as the Sun)

Again, see the difference? How small a million is (”down the street”) compared to the size of the Sun?

These numbers come in handy in many applications:

• 99.999% reliability (”Five 9’s”) means an error rate of 10 out of a million. That is, you can be offline for only 10 seconds every 12 days. Or, you can have a tolerance of 10mm for every kilometer. That’s pretty accurate!
• “One part per million” is often used by chemists to measure concentrations of substances. One ppm is like having a presence of 1 second in 12 days. And a part per trillion? You got it: 1 second every 30,000 years. That’s tiny.

This apprach helped me understand how utterly gigantic a trillion is, and how precise 99.999% really is.

Source: Mental Math Shortcuts