Here’s a collection of time-saving math shortcuts, great for
back-of-the-envelope estimates.
Time and Distance
60 mph = 1 mile per minute
- Going 60 mph and the exit is in 10 miles? That’s 10 minutes.
- Been driving a half hour? That’s about 30 miles at highway speeds.
Feet Per Second = MPH *
1.5
MPH = Feet Per Second *
2/3 (derivation)
- 60 mph is about 90 feet per second (88 exactly), so just multiply by 1.5.
Or, just add half to itself (60 + 30 = 90).
- Going 100 mph? That’s 150 fps.
- Going 10 fps? That’s about 7 mph (10 * 2/3 is 6.666). Or, just take away 1/3
(10 - 3 = 7).
speed of light = 1 foot per nanosecond (derivation)
- The US is about 3000 miles long. There’s about 5000 feet/mile, so that’s
about 3000 × 5000 or 15 million feet. 15 million feet takes 15 million
nanoseconds, or 15 / 1000, or 15 milliseconds. That’s the minimum latency for a
signal across the country.
- Inside a microchip, if you have a clock cycle every nanosecond (1 GHz), your
signal can only travel 1 foot. Distances matter.
1 year = 250 work days = 2000 work hours (derivation)
- Project takes 1000 man hours? That’s 6 months for 1 person.
- Daily commute of 1/2 hour? That’s .5 * 250 = 125 hours in the car each year.
Money and Finance
$1/hour = $2000/year (derivation)
- Earn $25/hour? That’s about 50k/year.
- Make 200k/year? That’s about $100/hour. This assumes a 40-hour work week.
$20/week = $1000/year (derivation)
- Spend $20/week at Starbucks? That’s a cool grand a year.
Rule of 72: Years To Double = 72/Interest Rate (derivation)
- Have an investment growing at 10% interest? It will double in 7.2 years.
- Want your investment to double in 5 years? You need 72/5 or about 15%
interest.
- Growing at 2% a week? You’ll double in 72/2 or 36 weeks. You can use this
rule for any duration of time, not just years.
- Inflation at 4%? It will halve your money in 72/4 or 18 years.
Mental Arithmetic
10,000 = hundred hundred
million = thousand
thousand
billion = thousand
million
trillion = million million
- 1% of 10k is 100. The Dow is roughly 10k (it’s about 12k now). So if the dow
drops 100, it’s about a 1% loss.
- What’s 5k x 50k? That’s 250 * thousand * thousand or 250 million.
2^6 = 64 (the sixes match: six and
sixty-four)
2^10 ~ thousand (1 kb)
2^20
~ million (1 mb)
2^30 ~ billion (1 gb)
- Sure, 2 to the tenth = 1024, but 1000 is good enough for government work.
- Have 32-bit color? That’s 2 + 30 bits, aka 2^2 billion, or 4 billion (4gb
exactly).
- Have a 16-bit number? That’s 6 + 10 bits, or 2^6 thousand, or 64 thousand
(64 kb).
a% of b = b% of a
- It’s not immediately clear, but it’s true: a% of b = a/100 * b, which is the
same as b% of a (b/100 * a).
- What’s 16% of 25? The same as 25% of 16: 4
- What’s 43% of 200? Same as 200% of 43: 86.
Reference: http://betterexplained.com/articles/mental-math-shortcuts/
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