In addition to unit analysis with the chain-link technique can also assist us come answer daunting questions. For example, calculating how countless heart win an average person experiences throughout their life time seems daunting. With the chain-link method we have the right to come up through an approximated value fairly quickly. A search of the internet finds that the average life expectancy in the U.S. Is 78.8 years<1> and that the usual value because that adult heart price is between 60 **BPM** and 100 **BPM**<2> so let’s take it the middle-range value of 80 **BPM** and go from there.

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### Everyday Examples: love Beats per Lifetime

We start with the median lifespan, i beg your pardon we will round come 80 years because that simplicity:

We have approximated that one lifetime will save on computer over three billion beats!

That’s a big number! In fact, that over 3 billion beats. As it turns out, human beings are fairly special among animals in the number of heartbeats per life time we experience. Visit the website that the beats per life time project<3> for much more information and an interaction look at heart rate statistics for various species.

In the ahead calculation we made decision to use a heart price of 80 **BPM**, which to be an approximation rather than an yes, really measurement or calculation. Therefore, our answer is only an estimate. However, we don’t intend anyone who lives to adulthood will get anywhere near 10x much more or 10x fewer beats 보다 this, so our answer is within an order of magnitude of what most world experience. Combine several currently known, easily found, or approximate worths to get a general idea that how large an answer have to be, as we just did because that beats per lifetime, provides anorder of magnitude estimation** . **Play through this simulation to exercise estimating size using just visual cues.

Order of magnitude estimation frequently relies on approximate values, so *order that magnitude calculation *and approximation are often used interchangeably. Including to confusion, approximation is regularly used interchangeably with presumption or offers approximation to explain a quick, stormy measurement with a high level of uncertainty. In order come maximize clarity this textbook will strive to stick to making use of terms as defined according to the complying with table.

Term | Definition | Everyday Example |

Assumption | Ignoring some compilation the the in order to simplify the evaluation or proceed even though details is lacking. Scientists state assumptions, justification why they to be needed, and estimate their possible impact ~ above results. | My cotton garments are fully soaked through, so ns assume they are not providing any kind of insulating effect versus the cold water. |

Approximation Approximate | Act of coming up v a rough value making use of prior knowledge and assumptions, yet not by do a measurement for the function of determining the value. | The water feels cold, but not shocking, similar to the 70 °F swimming lake, for this reason the almost right water temperature is 70 °F. |

Uncertainty (more about this later) | Amount through which a measured, calculated, or approximated value might be different from the yes, really value. | 85 °F would feel comfortable choose the 82 °F university pool and also 55 °F feels very cold, therefore + 15 F° is my suspicion from 70 °F. |

Order of size Estimate | Result of combine assumptions, almost right values, and/or measurements with huge uncertainty to calculate response with large uncertainty, but has the exactly order the magnitude. | Using known data, I estimated my time to exhaustion or loss of consciousness to it is in 5 hrs (less than 50 hours and an ext than 0.5 hours). See more: How And Why Do Ionic Bonds Dissolve In Water ? How Do Ionic Bonds Dissolve In Water |

Considering that our win per lifetime answer is just an bespeak of magnitude estimation, we have to round our final answer to have fewer far-reaching figures. Let’s make it 3,000,000,000 win per lifetime (**BPL**), or three billion **BPL**. A bit later in the chapter we will specify what we average by and significant figures and also talk more about why, when, and also how we have to do this kind of rounding. For now, we notice that it’s a little bit distracting and also a little annoying composing out every those zeros, therefore by counting that there space nine places prior to the first digit we deserve to use clinical notation and instead write:

**BPL**.Alternatively we deserve to use a metric prefix. The prefix because that 109 is Giga (

**G**) for this reason we have the right to write: 3

**(read as gigabeats per lifetime). The table listed below shows the common metric prefixes. For a much much more comprehensive perform of prefixes visit the NIST website. One advantage of making use of metric units is that the various size units space related straight by determinants of ten. For example 1 meter = 100**

*GBPL***cm**rather than 1 foot = 12 inches.Table the Metric Prefixes and also Representative Physical quantities 1

Prefix | Symbol | Value | Example (some space approximate) | |||

exa | E | 1018 | exameter | Em | 1018m | distance light travels in a century |

peta | P | 1015 | petasecond | Ps | 1015s | 30 million years |

tera | T | 1012 | terawatt | TW | 1012W | powerful laser output |

giga | G | 109 | gigahertz | GHz | 109Hz | a microwave frequency |

mega | M | 106 | megacurie | MCi | 106Ci | high radioactivity |

kilo | k | 103 | kilometer | km | 103m | about 6/10 mile |

hecto | h | 102 | hectoliter | hL | 102L | 26 gallons |

deka | da | 101 | dekagram | dag | 101g | teaspoon of butter |

– | – | 100 =1 | – | – | – | |

deci | d | 10-1 | deciliter | dL | 10-1L | less than fifty percent a soda |

centi | c | 10-2 | centimeter | cm | 10-2m | fingertip thickness |

milli | m | 10-3 | millimeter | mm | 10-3m | flea at its shoulders |

micro | µ | 10-6 | micrometer | µm | 10-6m | detail in microscope |

nano | n | 10-9 | nanogram | ng | 10-9g | small speck of dust |

pico | p | 10-12 | picofarad | pF | 10-12F | small capacitor in radio |

femto | f | 10-15 | femtometer | fm | 10-15m | size that a proton |

atto | a | 10-18 | attosecond | as | 10-18s | time light the cross an atom |