by Jennifer M. Wenner, Geology Department, college of Wisconsin-Oshkosh Jump under to: Teaching tactics | materials & exercises | college student Resources

What is scientific notation?

The principle of very huge or very tiny numbers is something that is complicated for numerous students come comprehend. In general, student have challenge with two points when dealing with numbers the have an ext zeros (either before OR after ~ the decimal point) 보다 they are supplied to. They often do not understand:

that "big" and also "small" are loved one terms, the ide of "order the magnitude"

Scientific notation is a method to assess the bespeak of magnitude and to visually diminish the zeros that the college student sees. It likewise may assist students to compare very big (or very little numbers) but students quiet have tiny intuition about scientific notation. Teaching them to identify that scientific notation is a short hand method to much better understand large and little numbers have the right to be helpful to lock in all aspects of their scholastic career.

it seems prefer a the majority of work to store track of every those zeros. Fortunately, us can conveniently keep track of zeros and compare the dimension of numbers with scientific notation.

Scientific notation enables us to reduce the number of zeros the we watch while still maintaining track of them because that us. For example the age of the earth (see above) deserve to be created as 4.6 X 109 years. This means that this number has actually 9 areas after the decimal ar - filled through zeros unless a number comes after the decimal as soon as writing scientific notation. So 4.6 X 109 year represents 4600000000 years.

Very little numbers usage the same form of notation just the exponent ~ above the 10 is normally a an adverse number. For example, 0.00000000000000000000000000166 kg (the load of one atomic mass unit (a.m.u.)) would certainly be created 1.66 x 10-27 using clinical notation. A an adverse number after the 10 way that us count places prior to the decimal allude in the clinical notation. You deserve to count how numerous numbers are between the decimal allude in the an initial number and also the second number and also it should equal 27.

The pretty thing around scientific notation is the it likewise tells us something about significant figures.


There space a number of geologic contexts in which large (and small) numbers and scientific notation come up. A couple of of castle include: The metric mechanism

Because anyone has various ways the learning, mathematicians have identified a variety of ways that quantitative concepts can be stood for to individuals. Below are some means that large numbers and also scientific notation can be represented.

You are watching: A type of notation used to express very large

Verbal representation
We represent big (and small) numbers v modifiers that tell united state how plenty of zeros space attached come the number. One million (1. X 106) tells united state that the decimal (after the 1) moves 6 locations to the right (1,000,000.). One thousandth (1. X 10-3) tells united state that the decimal move 3 spaces come the left (0.001).
Show list of numbers and also their modifiers
number power the ten modifier word
0.000001 10-6 millionths
0.0001 10-4
0.001 10-3 thousandths
0.01 10-2 hundreths
0.1 10-1 one per 10
1 100
10 101
100 102 hundred
1,000 103 thousands
1,000,000 106 million
1,000,000,000 109 billion
1,000,000,000,000 1012 trillion

4.5 X 109 yrsor (on a calculator) 4.5E9 yrs (1 exchange rate in scientific notation method 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10!)
Although plenty of topics in geoscience use scientific notation, graphical depictions are often plotted ~ above logarithmic scales as in the electromagnetic spectrum below.

there are numerous reasons because that this - most importantly, it takes up less an are - but a log scale does not give a feeling of true scale:
Geologic time is a great context in i beg your pardon to speak about huge numbers and to give a feeling of scale. We have the geologic time range to offer students a feeling of what parts of "time" we know the most about. And how big "time" really is. Below is a geologic time range that offers a sense of range
that is interesting to keep in mind that the time durations that we know the most around (the Cenozoic, Mesozoic and Paleozoic) only comprise a small portion of the totality of geologic time!
There space a number of analogies for thinking about big numbers. Student (particularly in entry-level classes) frequently relate fine to analogies through money: Money analogies: A local radio terminal is tring to collect a million pennies for a worthy cause. How many dollars is this? Answer: $10,000. You have actually just won a contest. The prize is that you will gain $1 receipt from a bank teller in ~ the price of 1 per 2nd for as long as you deserve to stand there taking them (no restroom breaks, no napping, etc.). Exactly how long will certainly you have to stand there to end up being a millionaire? Answer: about 12 days.
Students have actually a variety of tools that have the right to be offered to assist them become much more familiar through both scientific notation and very big and very tiny numbers. Calculators deserve to be collection up to display scientific notation. Spreadsheet programs deserve to tabulate data, expressing it in a number of forms. Calculators:
scientific notation provides fantastic way for students to end up being familiar with their (probably new) calculators. Plenty of students perform not understand what clinical notation is and also have small intuition about it. Also fewer really know how to usage their calculators come express it. Regularly I view students simply ignoring "the small number in the upper right" and so your answer is turn off by assignment of magnitude. Have actually students figure out just how to make their calculators express scientific notation. A rapid exercise to carry out in course is have them multiply part numbers in scientific notation on their calculator and also then compose the answer in numerical notation.
plenty of spreadsheets can be formatted to display screen numbers numerically and in clinical notation. Showing students a table of these data to express both methods may help them to obtain a feeling of what is keep going "in your calculators" once numbers are shown in scientific notation. This numbers can likewise be plotted so the students can obtain a sense of scale.

Mathematicians additionally indicate that students find out quantitative concepts much better when they job-related in groups and revisit a principle on an ext than one day. Therefore, when pointing out quantitative concepts in entry-level geoscience courses, have students comment on or practice the principles together. Also, make sure that you one of two people include problems that may be expanded over an ext than one class duration or revisit the principle on many occasions.

Very huge and very tiny numbers come increase over and over in introductory geoscience: Geologic time, radiometric dating, unit counter (especially metric), etc. As soon as each brand-new topic is introduced, make sure to point out that this is not brand-new material, it's simply a issue of remembering.

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MathWorld has actually a more mathematical explanation (more info) of scientific notation through a attach to significant digits (more info) .