How do I convert this with dimensional analysis? (ml to cm^3)?

the problem is

2 ml =______cm^3

how do i do that. like I KNOW that 1 ml = 1 cm^3

like the answer would be 2 cm^3 right?

but how do i show the work with dimensional analysis?

2 Answers

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  • Dr W
    Lv 7
    1 decade ago
    Best Answer

    2 ml x (1 cm^3 / 1 ml) = 2 cm^3

    read this...

    The process I used is called "unit factor method" aka "factor label method" and sometimes called "dimensional analysis"... it is one of the most important techniques you will learn in chemistry. it allows you to do unit conversions while watching the units cancel. Which prevents many common errors. It also allows you to change compound units easily...like kg m/s² to lb ft / s² for example...

    ************************************

    "unit factor method" explained

    ************************************

    take each of theses rules 1 at a time and read them thoroughly until you understand them. once you do, move on to the next...email me if you have questions...(you can email me via the link on my profile page).

    rule 1) units on top and bottom of a fraction cancel.

    examples:

    in / in = 1

    ft / ft = 1

    cm / cm cancels.

    sec / sec cancel

    sec² / sec² cancel

    m³ / m³ cancels

    got that down?

    ****

    rule 2) any number x 1 = that number

    examples:

    4 x 1 = 4

    4 in x 1 = 4 in

    5280 ft x 1 = 5280 ft

    9.8 m / s² x 1 = 9.8 m / s²

    easy right?

    ****

    rule 3) any equality can be rearranged to = 1

    examples:

    2.54 cm = 1 in

    if we divide both sides by 2.54 we get

    2.54 cm / 2.54 cm = 1 in / 2.54 cm

    1 = 1 in / 2.54 cm

    12 in = 1 ft

    12 in / 12 in = 1 ft / 12 in

    1 = 1 ft / 12 in

    also... since 1/1 = 1....

    1 / 1 = 1 / (1 ft / 12 in)

    1 = 12 in / 1 ft

    meaning for any equality of the form a = b, .....a / b = b / a = 1

    a/b and b/a are called unit factors because they = unity and we will be using them in rules 4 and 5 to factor (or more precisely "change" units)

    ok? this may be a bit more complicated than the first two rules but if you play around with it for a while I'm sure you will get it.

    ****

    rule 4) units can be changed by multiplying by an appropriate "unit factor".

    this essentially combines rules 1, 2, and 3

    example....

    10 in = ? cm

    10 in x 1 = 10 in right?

    and 2.54 cm / 1 in = 1 right?

    substituting

    10 in x (2.54 cm / 1 in ) = 10 x 2.54 x in x cm / in = 25.4 cm

    because inches cancel....

    3 ft = ? in

    3 ft x 1 = 3 ft x (12 in / ft) = 36 in

    here is an important trick... if the units you want to cancel are on the top, put the matching units for the "unit factor" on the bottom.. and vice versa. if on the bottom, then put the matching ones one the top....

    this will definitely take practice...

    ****

    rule 5) exponents....

    since 1 to any power = 1... any "unit factor" raised to any power = 1

    examples:

    1² = 1

    (2.54 cm / in) = 1

    (2.54 cm / in)² = 1² = 1

    similiarly

    (2.54 cm / in)³ = 1³ = 1

    how you use this is like this...

    10 in³ = ? cm³

    10 in³ x 1 = 10 in³ x (2.54 cm / in)³

    = 10 in³ x (2.54 cm)³ / (1 in)³

    = 10 in³ x 16.4 cm³ / 1 in³

    = 164 cm³

    645 ft³ = ??? in³

    645 ft³ x (12 in / ft)³ = 1.11 x 10^6 in³

    do you see that? 645 x 12³ = 1.11 x 10^6... ft³ / ft³ cancels... remaining units are in³

    645 ft³ = ??? m³

    645 ft³ x (12 in / ft)³ x (2.54 cm / in)³ x (1 m / 100 cm)³ = 18.3 m³

    645 x 12³ x 2.54³ / 100³ = 18.3...all the units have cancelled except for m³ right?

    and that's all there is to it...

  • 1 decade ago

    Ignore the dots, they're just for spacing

    2 ml..| 1 cm^3

    -------------------- = 2 cm^3

    ...1...|...1 ml

    the ml cancels out, leaving you with cm^2

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