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What is scientific notation?

The ide of very large or very small numbers is something the is challenging for numerous students to comprehend. In general, student have difficulty with two things when managing numbers that have much more zeros (either prior to OR ~ the decimal point) 보다 they are provided to. They regularly 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 order of magnitude and also to visually diminish the zeros the the student sees. It also may aid students to compare very large (or very tiny numbers) yet students quiet have small intuition about scientific notation. To teach them to recognize that clinical notation is a short hand means to better understand huge and tiny numbers have the right to be valuable to castle in all facets of their academic career.

You are watching: 4,600,000,000


that seems like a many work to save track of every those zeros. Fortunately, us can quickly keep track of zeros and compare the dimension of numbers with clinical notation.

Scientific notation permits us to reduce the number of zeros that we view while still maintaining track of them for us. For example the period of the earth (see above) can be created as 4.6 X 109 years. This way that this number has actually 9 places after the decimal place - filled through zeros uneven a number come after the decimal once writing clinical notation. Therefore 4.6 X 109 year represents 4600000000 years.

Very tiny numbers usage the same type of notation only the exponent top top the 10 is usually a an unfavorable number. For example, 0.00000000000000000000000000166 kg (the weight of one atom mass unit (a.m.u.)) would certainly be written 1.66 x 10-27 using clinical notation. A an adverse number after ~ the 10 way that we count places before the decimal point in the scientific notation. You can count how many numbers are in between the decimal suggest in the first number and also the 2nd number and also it must equal 27.

The nice thing about scientific notation is that it additionally tells us something about far-reaching figures.

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There room a number of geologic contexts in which big (and small) numbers and also scientific notation come up. A few of them include:

The metric device
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Because anyone has various ways that learning, mathematicians have identified a number of ways that quantitative principles can be represented to individuals. Here are some means that huge numbers and also scientific notation deserve to be represented.

Verbal representationNumerical representationGraphical representationSymbolic representation
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Students have a variety of tools that have the right to be supplied to help them become more familiar through both clinical notation and also very large and very tiny numbers. Calculators deserve to be collection up to display scientific notation. Spreadsheet programs deserve to tabulate data, expressing it in a variety of forms.

Calculators: Computers:
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Mathematicians also indicate that students discover quantitative concepts much better when they occupational in groups and revisit a ide on an ext than one day. Therefore, when mentioning quantitative principles in entry-level geoscience courses, have actually students talk about or practice the principles together. Also, make certain that you one of two people include problems that might be prolonged over an ext than one class duration or revisit the principle on many occasions.

Very huge and very tiny numbers come up over and also over in introduce geoscience: Geologic time, radiometric dating, unit counter (especially metric), etc. As soon as each new topic is introduced, make sure to suggest out the this is not new material, it's simply a matter of remembering.

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MathWorld has a much more mathematical explanation (more info) of scientific notation through a attach to far-reaching digits (more info) .