8 Heart Beats Per Lifetime
Estimating Lifetime Heart Beats
In addition to unit analysis, the chainlink method can also help us to roughly estimate the answer to difficult questions. For example, calculating how many heart beats an average person experiences during their lifetime seems daunting. With the chainlink method we can come up with an estimated value relatively quickly. A search of the internet finds that the average life expectancy in the U.S. is 78.8 years^{[1]} and that the typical value for adult heart rate is between 60 BPM and 100 BPM^{[2]} so let’s take the middlerange value of 80 BPM and go from there.
Everyday Examples: Heart Beats Per Lifetime
We start with the average lifespan, which we will round to 80 years for simplicity:
We have estimated that one lifetime will contain over three billion beats!
That’s a big number! In fact, it’s over three billion beats. As it turns out, humans are quite special among animals in the number of heartbeats per lifetime we experience. Visit the website of the beats per lifetime project^{[3]} for more information and an interactive look at heart rate statistics for various species.
In the previous calculation we chose to use a heart rate of 80 BPM, which was an approximation rather than an actual measurement or calculation. Therefore, our answer is only an estimate. However, we don’t expect anyone who lives to adulthood will get anywhere near 10x more or 10x fewer beats than this, so our answer is within an order of magnitude of what most people experience. Combining several already known, easily found, or approximate values to get a general idea of how big an answer should be, as we just did for beats per lifetime, provides an order of magnitude estimation. Play with this simulation to practice estimating sizes using only visual cues.
Estimation and Approximation
Order of magnitude estimation often relies on approximate values, so order of magnitude estimate and approximation are often used interchangeably. Adding to confusion, approximation is often used interchangeably with assumption or to describe a quick and rough measurement with a high degree of uncertainty. In order to maximize clarity this textbook will strive to stick to using terms as defined according to the following table.
Term  Definition  Everyday Example 
Assumption  Ignoring some compilation of the in order to simplify the analysis or proceed even though information is lacking. Scientists state assumptions, justify why they were needed, and estimate their possible impact on results.  My cotton clothes are completely soaked through, so I assume they are not providing any insulating effect against the cold water. 
Approximation

Act of coming up with a rough value using prior knowledge and assumptions, but not by making a measurement for the purpose of determining the value.  The water feels cold, but not shocking, similar to the 70 °F swimming lake, so the approximate water temperature is 70 °F. 
Uncertainty (more about this later)  Amount by which a measured, calculated, or approximated value could be different from the actual value.  85 °F would feel comfortable like the 82 °F college pool and 55 °F feels very cold, so + 15 F° is my uncertainty from 70 °F. 
Order of Magnitude Estimate  Result of combining assumptions, approximate values, and/or measurements with large uncertainty to calculate an answer with large uncertainty, but has the correct order of magnitude.  Using known data, I estimated my time to exhaustion or loss of consciousness to be 5 hours (less than 50 hours and more than 0.5 hours). 
Metric Prefixes
Considering that our beats per lifetime answer is only an order of magnitude estimation, we should round our final answer to have fewer significant figures. Let’s make it 3,000,000,000 beats per lifetime (BPL), or three billion BPL. A bit later in the chapter we will define what we mean by and significant figures and also talk more about why, when, and how we have to do this kind of rounding. For now, we notice that it’s a bit distracting and a bit annoying writing out all those zeros, so by counting that there are nine places before the first digit we can use scientific notation and instead write: BPL. Alternatively we can use a metric prefix. The prefix for 10^{9} is Giga (G) so we can write: 3 GBPL (read as gigabeats per lifetime). The table below shows the common metric prefixes. For a much more comprehensive list of prefixes visit the NIST website. One advantage of using metric units is that the different size units are related directly by factors of ten. For example 1 meter = 100 cm rather than 1 foot = 12 inches.
Prefix  Symbol  Value  Example (some are approximate)  
exa  E  10^{18}  exameter  Em  10^{18} m  distance light travels in a century 
peta  P  10^{15}  petasecond  Ps  10^{15} s  30 million years 
tera  T  10^{12}  terawatt  TW  10^{12} W  powerful laser output 
giga  G  10^{9}  gigahertz  GHz  10^{9} Hz  a microwave frequency 
mega  M  10^{6}  megacurie  MCi  10^{6} Ci  high radioactivity 
kilo  k  10^{3}  kilometer  km  10^{3} m  about 6/10 mile 
hecto  h  10^{2}  hectoliter  hL  10^{2} L  26 gallons 
deka  da  10^{1}  dekagram  dag  10^{1} g  teaspoon of butter 
–  –  10^{0} =1  –  –  –  
deci  d  10^{1}  deciliter  dL  10^{1} L  less than half a soda 
centi  c  10^{2}  centimeter  cm  10^{2} m  fingertip thickness 
milli  m  10^{3}  millimeter  mm  10^{3} m  flea at its shoulders 
micro  µ  10^{6}  micrometer  µm  10^{6} m  detail in microscope 
nano  n  10^{9}  nanogram  ng  10^{9} g  small speck of dust 
pico  p  10^{12}  picofarad  pF  10^{12} F  small capacitor in radio 
femto  f  10^{15}  femtometer  fm  10^{15} m  size of a proton 
atto  a  10^{18}  attosecond  as  10^{18} s  time light crosses an atom 
Reinforcement Exercises
act of ensuring that the units resulting from a calculation match the type of quantity calculated.
a specific method for unit conversion that is designed to aid in reducing mistakes.
a rough value obtained without making a measurement by using prior knowledge and assumptions.
designating which power of 10 (e.g. 1,10,100,100)
the process of approximating a value to obtain a result you expect to at least be within one order of magnitude of the correct answer.
ignoring some compilation of the in order to simplify the analysis or proceed even though information is lacking
Amount by which a measured, calculated, or approximated value could be different from the actual value
each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit
a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit