Scientific Notation Rules and Examples

by
Ahmed Faizan

The goal of this module is to provide students with the tools they need to use scientific notation to represent quantities, apply electrical units of measure, convert metric units, and express measured data with the proper number of significant figures.

Objective

A learner will be able to:

  • Use scientific notation to represent quantities
  • Convert one electrical metric unit to another metric unit
  • Convert from one unit with a metric prefix to another unit using scientific notation
  • Express measurements with the proper number of significant figures.

Orienting Questions

  • How do you represent extremely large or small quantities using scientific notation?
  • What are the processes of performing arithmetic using scientific notation?
  • How do you convert measurements containing metric prefixes?

Introduction

When dealing with extremely large or small quantities, scientists and engineers use scientific notation as a form of representation.  In electronics, scientific notation is an important tool for representing electrical values. Important skills include being able to perform arithmetic (adding, subtracting, multiplying, and dividing) using scientific notation, and being able to convert between units of metric measures.

Quantities represented by the Scientific Notation

Very large and very small quantities are encountered a great deal in electronics.  Scientific notation is used in the place of huge numbers of digits. 

Scientific notation is a convenient way to express large or small numbers in order to perform arithmetic and other functions.  It uses a base number between 1 and 10, and a power of ten.  A power of ten is a representation of a base number of ten and an exponent indicating how many times the base number is raised. The power of ten is represented by a symbol written above and to the right of a digit, or an exponent.

For example, if we were to represent 230,000 in scientific notation, we would move the decimal point left until we have a number between 1 and 10 on the left side of the decimal.

In this case, we would move the decimal point between the 2 and 3.

Next, we would count the number of digits to the right of the decimal.  In our example, there are 5.  So 230,000 would be represented as 2.3 X 105.

Scientific notation can only have a number less than 10 to the left of the decimal.  Any numbers to the right of the decimal, greater than zero, must remain in the base number.  As in the above example, we left the 3 in the base number since it is greater than zero.

To convert a number represented by scientific notation to a decimal number, we would simply move the decimal to the right the number of places indicated by the exponent.

Example         

            Let’s take the following number and convert it to scientific notation:

2,500,000        Our number

2.5                   We place our decimal between the 2 and 5 which gives us our base number between 1 and 10.

2.5 X 106         We moved the decimal 6 places to the left.

 Small Numbers

When dealing with small numbers, the decimal is moved to the right.  Instead of a positive exponent (power of ten), it is negative.  This does not mean the number is negative.

For example, if we wanted to represent the quantity 0.00000362, we would move the decimal to the right until we have a number between 1 and 10.  In this case, our decimal would be between the 3 and 6.

Next, we would count how many digits are on the left side of the decimal.  In our example, we moved the decimal 6 places.  Our example would be 3.62 X 10-6.

Notice, we left the 2 because it is a number greater than zero.

To convert a small number represented by scientific notation to a decimal number, we move the decimal to the left the number of places indicated by the exponent.

Example

            Let’s represent the following decimal number in scientific notation:

0.000 000 025               our number.

2.5                               We moved the decimal point to the right to give us our base of 2.5 which is between 1 and 10.

2.5 X 10-8                      We moved the decimal 8 places to the right, giving us our exponent of (-8).

More examples

            516,570,000,000,000 = 5.1657 X 1014

            0.000100972 = 1.00972 X 10-4

            4,683.8 = 4.6838 X 103

            0.05871 = 5.871 X 10-2

           7.55 X 102 = 755                    

            190 X 106 = 190,000,000                   

            1.23 X 10-6 = 0.00000123                  

            9 X 10-3 = 0.009                     

View the video below before proceeding to the next section.

Scientific Notation Video

Arithmetic with scientific notation       

Scientific notation makes performing arithmetic simpler when dealing with very large and very small numbers.  This leaves less room for errors.

Addition

We add numbers in scientific notation using the following method:

  1. Express both numbers with the same power of ten.
  2. Add the base numbers.
  3. Bring the power of ten down to represent the new power of ten for the sum.
  4. Simplify so that the base number is between 1 and 10.

Example

How would we add 3 X 105 plus 6 X 104?

We need to first express the numbers using the same power of ten: 

            (3 X 105) + (60 X 105)

Add the base numbers:

            3 + 60 = 63

Bring the power of ten down:

            63 X 105

Simplify so that the base is a number between 1 and 10:

            6.3 X 106

Subtraction

The following method is used when subtracting powers of ten:

  1. Express both numbers with the same power of ten.
  2. Subtract the base numbers without their power of ten.
  3. Bring the power of ten down to represent the difference.
  4. Simplify so that the base number is between 1 and 10.

Example

Here is an example of subtracting numbers expressed in powers of ten:

            Subtract 3.5 X 10-12 from 9.5 X 10-11

First we represent both numbers in the same power of ten:

            (9.5 X 10-11) – (.35 X 10-11)

Subtract the base numbers:

            9.5 – .35 = 9.15

Bring down the power of ten:

             9.15 X 10-11 

Scientific Notation: Addition and Subtraction

Multiplication

To multiply numbers expressed in scientific notation use the following method:

  1. Multiply the base numbers without their powers of ten.
  2. Add the powers of ten using the algebraic rules for adding numbers (the exponents do not need to be the same).

Example

Multiply 6 X 103 by 4 X 10-5

Multiply the base numbers:        (6)(4) = 24

Add the exponents:                 3 + (-5) = -2

The product is:                        24 X 10-2

Simplified:                             2.4 X 10-1

Division

To divide numbers expressed in scientific notation use the following method:

  1. Write the problem as a fraction with a numerator and denominator.
  2. Divide the base numbers.
  3. Subtract the exponent in the denominator from the exponent in the numerator (the exponents do not need to be the same).

Example

Divide 7 X109 by 3.5 X 104:

            Represent problem as a fraction:      

$\frac{7~X~{{10}^{9}}}{3.5~X~{{10}^{4}}}$

            Divide the base numbers:

                                                                        7 / 3.5 = 2

            Subtract the exponents:

                                                                        9 – 4 = 5

The quotient is:                                  2 X 105

Scientific Notation: Multiplication and Division

Converting Measures with Metric Prefixes

In the electronics field, you will deal with measureable quantities.  You will measure voltage, current, and resistance as well as many other electrical quantities.  All of these measurements have certain units and symbols that are used in combination with engineering notation.

Engineering Notation

Similar to scientific notation, engineering notation uses the same “power of ten” concept.  A difference is that engineering notation can have up to three digits to the left of the decimal.  Also, engineering notation can only have exponents that are multiples of three (3, 6, 9, etc.).

Example

Below are a few examples of numbers represented by both scientific and engineering notations:

Number                                   Scientific notation                  engineering notation 

23,000                                     2.3 X 104                                       23 X 103

500                                          5 X 102                                    500 or .5 X 103

0.000052                                 5.2 X 10-5                                52 X 10-6

Electrical Units

Electrical units and quantities are represented by a letter symbol.  Below is a table of some common electrical quantities, SI (International Standard), and symbols:

QUANTITY SYMBOL SI UNIT SYMBOL
Voltage V Volt V
Current I Ampere (Amp) A
Charge Q Coulomb C
Resistance R Ohm Ω
Capacitance C Farad F
Inductance L Henry H
Power P Watt W
Energy W Joule J
Time T Seconds S
Frequency F Hertz Hz 


Primer on Electrical Units, Abbreviations and Symbols 1-2

Metric Prefixes

Metric prefixes represent some of the most common powers of ten in engineering notation.  Below is a table showing the most common metric prefixes:

Prefix Prefix
Symbol		 Value
Pico P 10-12 = 0.000 000 000 001
nano n 10-9 = 0.000 000 001
micro µ 10-6 = 0.000 001
milli m 10-3 = 0.001
kilo k 103 = 1000
Mega M 106 = 1000 000
Giga G 109 = 1000 000 000
Tera T 1012 = 1000 000 000 000

Example

            Show the following number with the prefix and the unit symbols:

                        0.005 Volts     Our number

                        5 X 10-3           Volts in scientific notation

                        5 m Volts        On our table we see 10-3 is represented by m

                        5 mV               The symbol for volts is V

Converting Metric Units

In order to do some calculations involving metric units, it is more convenient to convert the metric prefixes.  There are some basic guidelines to follow when converting prefixes:

  1. Move the decimal point to the right when converting large units to smaller units.
  2. Move the decimal point to the left when converting small units to larger units.
  3. Find the difference of the powers of ten to decide how many places to move the decimal point.

Example

  1. Convert 3 millifarads to microfarads.

Using the table above, we see that mF is millifarads (10-3).  Microfarads is 10-6.  Since microfarads are smaller than millifarads we would move the decimal three places to the right.  This would give 300µF.

  1. Convert 4000 nanoamperes to microamperes.

                   We would move the decimal three places to the left.

                  4000nA = 4000 X 10-9A = 4 X 10-6 = 4µA

  1. Convert 1600 Kilohms to Megaohms

We would move the decimal three places to the left.

1600kΩ = 1600 X 103 = 1.6 X 106  = 1.6MΩ

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  401. The examples on moving the decimal and preserving significant figures make metric conversions much easier to follow, especially for electrical values. When exporting worksheets or lab reports as PDFs, PDF Meta Editor could also help verify or remove metadata locally before sharing sensitive measurement files.

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  403. I really appreciated how this module breaks down scientific notation into such clear, manageable steps—especially the part about applying it to electrical units. It’s one of those topics that can feel intimidating at first, but the examples make it click. I remember struggling with very small numbers in my own projects, and having a solid reference like this would have saved me so much time. Speaking of saving time, if you’re sharing or storing images of your circuit diagrams or notes, you might want to check out Remove AI Metadata from Photos to keep your files clean. It’s a small step that makes a big difference when you’re organizing technical documentation. For anyone who wants to explore this further, Metadata Remover AI may also be a useful resource.

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  427. Great resource for mastering scientific notation—especially for electrical engineering students! If you’re also exploring how AI models interpret and generate real-world physical systems (like circuits or signal behaviors), check out worldmodelswatch.com/
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  468. I found the explanation of how to handle exponents when multiplying and dividing scientific notation really helpful. It’s something I always trip up on, so seeing it laid out clearly with examples makes a big difference for me.

  470. This is a clear and practical introduction to scientific notation – a fundamental skill for anyone working in electronics, engineering, or the sciences. The module covers key areas like representing large and small quantities, performing arithmetic in scientific notation, converting metric units, and applying significant figures correctly. These are foundational tools that students and professionals alike need to master. It’s a reminder that precision and clarity matter in every technical field – which is why we offer acrylic display cases wholesale – because whether you’re working with numbers or displaying products, accurate representation and clear presentation are essential.

  471. В этом клубе игроки из разных стран получают моментальную выплату выигрышей на карту или электронный кошелёк.

  472. НА сегодняшнем подлунной, кае посещение ко различным веществам встал проще благодаря интернету, почти многие заниматся проблемой получения наркотических веществ.
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    в течение различных кругах.

    Гашиш и марихуана предполагают собою растительные ядовитый дурман, получаемые из конопли.
    Ихний использование имеет глубочайшие многознаменательные корешки,
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    не в полной мере на SUAVITY многих
    краев, стимулируя обсуждения яко
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    из конопли. Ихний эксплуатация располагает глубокие исторические корни,
    а также в течение крайние десятилетия они
    встали не в полной мере в SUAVITY почти всех держав, пробуждая обсуждения
    как в плюсе, яко и в минусе.
    Яко узаконенный, яко а также нелегальный ярмарка этих веществ не прекращает взращивай, приковывая как потребителей,
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    Также следует отметить мефедрон, яже якобы небиологическим наркотиком (а) также иметь
    в распоряжении свои особенности в течение происхождении а
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    среди молодого поколения, что ни говорите евонный узаконенность
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    В ТЕЧЕНИЕ этой посте да мы с
    тобой рассмотрим ярмарка продажи гашиша, марихуаны,
    мефедрона и их популярность
    среди потребителей. Понимание данных аспектов подать руку помощи образовать более беспристрастное мнение что касается
    существующих рисках а также возможностях, связать руки вместе с потреблением данных веществ.

    Кае почерпнуть ямба: легальные а также подпольные список источников

  476. В нынешнем подлунной, кае путь для всевозможным препаратам
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    проблемой приобретения наркотических
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    известностью продуктам, как ямба, марихуана и еще мефедрон, коим широкошенько обсуждаются в течение разных кругах.

    Гашиш также трава представляют собою постные наркотики, получаемые из конопли.

    Их использование располагает глубокие исторические
    корешки, а также в крайние десятилетия город стали в известной мере на TASTE многих держав,
    возбуждая обсуждения как в плюсе, так и в течение минусе.
    Как легальный, так а также нелегальный ярмарка
    сих материалов не прекращает расти, притягивая яко потребителей, яко и продавцов.

    Также следует отметить мефедрон, который считается искусственным наркотиком (а) также иметь в своем
    распоряжении собственные особенности
    на происхождении а также действии.

    Спирт вызывает самый большой интерес среди молодежи, однако его узаконенность
    и последствия использования остаются темой жарких споров.

    НА данной посте наш брат рассмотрим рынок торговли гашиша, марихуаны,
    мефедрона а также ихний популярность средь потребителей.

    Чувствование данных ньюансов подать руку помощи основать
    сильнее беспристрастное мнение
    о имеющихся рисках равным образом потенциалах, связанных вместе с употреблением данных веществ.

    Где завести ямба: легальные и
    еще нелегальные список литературы

  478. В сегодняшнем подлунной, где посещение ко неодинаковым веществам итак элементарнее благодаря вебу, многие интересуются вопросом получения наркотических веществ.
    Специальное внимание уделяется таким модным
    провиантам, яко гашиш, трава равным образом мефедрон, тот или иной широко
    обсуждаются на разных кругах.

    Гашиш да марихуана играют собою постные ядовитый дурман,
    получаемые изо конопли. Их эксплуатация содержит глубочайшие исторические
    корешки, также в последние десятилетия они стали не в полной мере в течение
    CULTURE почти всех государств, возбуждая обсуждения как в плюсе, так и в минусе.

    Как узаконенный, так да черный ярмарка данных веществ продолжает расти,
    притягивая как потребителей, яко (а) также продавцов.

    Также стоит пометить мефедрон, яже якобы синтетическим наркотиком (а) также владеет свои
    особенности в течение происхождении а также действии.

    Он разгоняет самый большой энтузиазм среди молодых людей, однако евонный узаконенность
    и еще последствия пользования остаются предметом горячих
    споров.
    В ТЕЧЕНИЕ этой статье наш брат рассмотрим рынок объемы продажи гашиша, марихуаны, мефедрона а также их
    популярность среди потребителей.
    Чувствование сих ньюансов подать руку помощи основать сильнее беспристрастное
    философема о имеющихся рисках равным образом возможностях, связать руки начиная с.
    ant. до потреблением данных веществ.

    Кае почерпнуть ямба: озагсенные и подпольные источники

  479. В ТЕЧЕНИЕ нынешнем подлунной,
    где путь буква всевозможным веществам стал проще через интернету, почти многие заниматся
    вопросом приобретения наркотических веществ.
    Особое чуткость уделяется этаким модным продуктам, яко гашиш, трава и мефедрон, тот или
    иной широко обсуждаются
    в течение различных кругах.
    Гашиш и трава играют собою постные
    наркотики, получаемые изо конопли.

    Ихний использование быть обладателем глубокие исторические корешки, также на последние десятилетия город следовательно частью в
    течение TASTE почти всех краев, стимулируя обсуждения
    яко на плюсе, яко также на минусе.
    Яко узаконенный, так да нелегальный рынок этих материалов
    продолжает вытягиваться, соблазняя
    как потребителей, так и еще продавцов.

    Также стоит отметить мефедрон, яже якобы
    небиологическим наркотиком и имеет собственные особенности в происхождении
    (а) также действии. Спирт вызывает наибольший энтузиазм средь молодежи, что ни говорите
    евонный легальность и еще исходы потребления остаются дисциплиной горячих споров.

    НА данной посте наш брат разглядим ярмарка реализации
    гашиша, марихуаны, мефедрона и ихний читаемость средь потребителей.
    Понимание этих ньюансов поддержит образовать более
    объективное мнение о существующих рисках а также возможностях,
    сцементированных с употреблением этих веществ.

    Где завести гашиш: озагсенные а также
    подпольные литература

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