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2.7: SI Prefixes

  • Page ID
    266483
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    Introduction

    We have all heard of SI prefixes, for example you may have a 16 Gbyte flash drive, where the G stands for giga and means 109, and that is a much more convienent way of expressing the number of bytes than using the floating number of 16,000,000,000 bytes.  Chemists need to be able to convert between different ways of expressing, but the first step is to memorize the unit definitions themselves.  It is important that you do this as you will not be able to follow the science later on in the course if you do not understand the meanings of the terms used.  It is like trying to write a sentence without knowing the alphabet  What you notice is that most of the units you are required to memorize are multiples of 103, and if you look at the above 16 Gbyte flash drive, when we wrote it as a floating decimal point number we placed a comma between every "000", which is 103,moved it up or down 1000 positions, so Giga (109), had 9 zeros with 3 commas.  The result is you can express any number with between 1 and 999 values to the left of the decimal, followed by the appropriate SI prefix.  So we would say 16 Gigabytes and not 16,000 Mbytes of 16,000,000 kbytes.

    The convention of using an SI prefix with a number between 1 and 999 is often called engineering notation and is a common way of representing very large and small numbers.

    SI Prefixes

    SI prefixs are commonly used to represent very large and small numbers. You need to memorize many of these and know how to convert between them.

    Table \(\PageIndex{1}\): SI prefixes. Note Chem 1300 students need to memorize all the values in red.
    Multiplier Name Abbreviation Name Multiplier
    10+30 quetta* Q q quecto* 10-30
    10+27 ronna* R r ronto* 10-27
    10+24 yotta Y y yocto 10-24
    10+21 zetta Z z zepto 10-21
    10+18 exa E a atto 10-18
    10+15 peta P f femto 10-15
    10+12 tera T p pico 10-12
    10+9 giga G n nano 10-9
    10+6 mega M m micro 10-6
    10+3 kilo k m milli 10-3
    10+2 hecto h c centi 10-2
    10+1 deca da d deci 10-1

    *quetta, ronna, ronto & quecto were added in 2022 (https://www.bipm.org/en/cgpm-2022/resolution-3).

    NOTE: The Angstrom is a common unit of length, 1 Å = 10-10m). It is not an SI prefix, but is a common unit of length that is used when describing bond lengths and distances between atoms (and ions) in a crystal.

    Use of SI prefixes

    For real large or small numbers, the convention is to place a number with between 1 and 999 in front of the SI prefix, and use the appropriate prefix to show the value. So a memory stick with 1,200,000 bytes would be written as 1.2 Mbyte, not as 1,200 kbytes.

    In a later section you are going to have to learn how to convert between SI units, or even between SI units and scientific notation.

    SI prefixes and Calculators

    What is the ENG key on scientific calculators?

    ENG-Calc.JPG
    Figure \(\PageIndex{8}\): Three display modes on TI 30 calculator.

    In Scientific Notation there is one digit to the left of the decimal, in Engineering notation there are 1, 2 or 3 digits to the left of the decimal, and you then use one of the Si prefixes that is of the magnitude 103n.

    \[ \begin{align}  1,330,000,000m & =1 .33 \times 10^{9}m  =1.33 \; gigameters \nonumber \\  13,300,000,000m & =13.3 \times 10^{9}m =13.3 \;gigameters \nonumber \\ 133,000,000,000m & =133  \times 10^{9}m  = \; 133 \; gigameters \end{align}\]

     

    The ENG key takes large or small numbers and expresses them as integer multiples of 103 or 10-3, effectively converting them to values that can be expressed with SI prefixes. If you type 1,200,000 into your calculator and press ENG, it gives 1.2 x 106, so 1,200,000 bytes of memory on a memory stick would be 1.2 MBytes (you do not say 1,200 kBytes). If you try 0.12 and press ENG, it gives 120 x 10-3, so 0.12g is 120 mg. So the ENG function quickly converts numbers to values that can easily be expressed with SI prefixes.

     

    Test Yourself

    Homework: Section 2.7

    The following activities are drill and practice.  You need to memorize the red SI prefixes in table \(\PageIndex{1}\).  Note, on the flash cards you can skip a card by clicking

    "I got it right" and can skip the ones you know.

    Activity \(\PageIndex{1}\)

     

    Flash cards that go from SI prefix name to value. NOTE: If you already know an answer you can just click "I got it right" and move on to the next.  Everytime you reload these should rearrange.

     

    Activity \(\PageIndex{2}\): Prefix to Value

     

    Flash cards that go from SI prefix value to name.  NOTE: If you already know an answer you can just click "I got it right" and move on to the next.  Everytime you reload these should rearrange.

     

    Activity \(\PageIndex{3}\): Value to Prefix

     

    Flash cards that go from SI prefix symbol to value. NOTE: If you already know an answer you can just click "I got it right" and move on to the next.  Everytime you reload these should rearrange.

     

    Activity \(\PageIndex{4}\): Abbreviation to Prefix

     

    Contributors and Acknowledgements

    • Robert E. Belford (University of Arkansas Little Rock; Department of Chemistry). The breadth, depth and veracity of this work is the responsibility of Robert E. Belford, rebelford@ualr.edu. You should contact him if you have any concerns. This material has both original contributions, and content built upon prior contributions of the LibreTexts Community and other resources, including but not limited to:

    • Elena Lisitsyna & Vincent Belford (H5P interactive modules)

    This page titled 2.7: SI Prefixes is shared under a not declared license and was authored, remixed, and/or curated by Robert Belford.

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