Standard form and Prefixes

physics

Standard form is a way of writing very small and large numbers. The numbers are written in the form clip_image002 ; where “a” is a number between 1 and 10, “m” is an integer (positive or negative) and “n” is base 10.

Examples:

  1. 0.00312 written in standard form =clip_image004 . Very small numbers are represented with negative integers, depending on the number of places move to the right in order to get a number between 1 and 10.
  2. 0.912 written in standard form= clip_image006 .Base 10 is raise to the power of negative -1, because only one place is move to the right.
  3. 980000 written in standard form=clip_image008. Base 10 is raise to the power of positive 5, because five places are moved to the left in order to obtain a number between 1 and 10 (9.8).
  4. 200.13 written in standard form=clip_image010. You will see that 2 places are moved to the left in order to obtain a number between 1 and 10 (2.0013) and that base 10 is raise to the power of positive 2. Why? Because only 2 place are move to the left.

    Prefixes Used in Science and Technology

    Name of Prefix

    Symbol

    Numerical Form

    Deka

    da

    101

    Hecto

    h

    102

    Kilo

    K

    103

    Mega

    M

    106

    Giga

    G

    109

    Tera

    T

    1012

    Peta

    P

    1015

    Exa

    E

    1018

    Zetta

    Z

    1021

    Yotta

    Y

    1024

    Prefixes Use in Science and Technology

    Name of Prefix

    Symbol

    Numerical Form

    Deci

    d

    10-1

    Centi

    c

    10-2

    Milli

    m

    10-3

    Micro

    µ

    10-6

    Nano

    n

    10-9

    Pico

    p

    10-12

    Femto

    f

    10-15

    Atto

    a

    10-18

    Zepto

    z

    10-21

    Yocto

    y

    10-24

How to Use Prefixes

Let’s say you worked out a physics question and you got 2million metres for your answer. You can write your answer in standard form or using prefixes. I will also show you the relationship between standard form and prefixes.

2million metres (2,000,000m) written in standard form= clip_image012 or written using prefix= 2Mn. Look at the prefixes table you will see that clip_image014 = Mega (M). So what happen is that clip_image014[1] is replace by “M” the symbol for Mega (clip_image016. So in dealing with very small and large numbers you can replace this part of the number “clip_image018” with the prefix connected to it. I hope that highlight the relationship between standard form and prefixes. Please look at the examples below.

1. 2900= clip_image020 (standard form)= 2.9K (k= kilo= clip_image022)

2. 0.098m (metre or meter) = clip_image024 = 9.8cm. Please note that “centi” which equal to “clip_image026” replace the clip_image026[1] written in standard form with its symbol “c”.

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