Question

4. Write conversion factors for each equality.
a. 1 m3 = 1 000 000 cm3
b. 1 in. = 2.54 cm
c. 1 ug = 0.000 001 g
d. 1 Mm = 1 000 000 m

Answer 1

Answer:

Conversion factors are defined as an ‘arithmetical multiplier’ in which one quantity expressed in one unit is equivalent to the quantity expressed in another units. The International System of Units have developed a system of measurement, which can be used worldwide in their derived forms.

Explanation:

Conversion factors are used to change one of units in another form that are equivalent. For example,  

$\begin{aligned}1^{3} &= 1000000 \; \text {cm}^{3} \\&= 10^{6} \text {cm}^{3} }\end{aligned}$

Also,  

Converting $1\;\text{cm}^{3}$ into $\text {m}^{3}$, the equation will be written as:

$\begin{aligned}1\text{cm}^{3} &= \dfrac{1}{1000000 \; \text {m}^{3} \\\\&= 10^{-6} \text {m}^{3} }\end{aligned}$

Similarly,  

$1\;\text {inch}&=\; 2.54 \;\text{cm}$

The value of one inch in centimetres is 2.54 centimetres. Therefore, converting the centimetres into inches, the conversion factor will be:

$1\;\text{cm} = 0.393 \;\text{inches}$

The conversion factor for 1 microgram to grams is 0.000001. now for converting grams into micrograms, the conversion factors will be:

$1 \;\text{gram} = 1000000 \;\text{micrograms}$

Similarly, for the next conversion factor, $1\;\text{ megametre}& = 1000000 \; \text{meter}$. The conversion factor for the meter to megametre will be:

$\begin{aligned}1\text{\;m}} &= \dfrac{1}{1000000 \; \text {Mm} \\\\&= 10^{-6} \text {Mm}} }\end{aligned}$

Answer 2

Conversion factor is simply the number that converts a unit to another unit. The conversion factors are:

• $10^6$ for $m^3$ to $cm^3$
• $2.54$ for $in$ to $cm$
• $10^{-6}$ for $\mu g$ to $g$
• $10^{6}$ for $Mm$ to $m$

Let:

$k \to$ conversion factor

$(a)\ 1\ m^3 = 1000000\ cm^3$

Cancel out both units.

$k = 1000000$

Express $1000000$ as exponent

$k = 10^6$

Hence, the conversion factor from $m^3$ to $cm^3$ is: $10^6$

$(b)\ 1\ in = 2.54\ cm$

Cancel out both units

$k = 2.54$

Hence, the conversion factor from $in$ to $cm$ is: $2.54$

$(c)\ 1\mu g = 0.000001g$

Cancel out both units

$k = 0.000001$

Express as exponents

$k = 10^{-6}$

Hence, the conversion factor from $\mu g$ to $g$ is: $10^{-6}$

$(d)\ 1Mm = 1000000m$

Cancel out both units

$k = 1000000$

Express as exponents

$k = 10^6$

Hence, the conversion factor from $Mm$ to $m$ is: $10^{6}$

Read more about conversion factors at:

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