Converting Between U.S. and Metric Systems of Measurement

Learning Outcomes

Convert between the U.S. and the metric systems of measurement
Convert between Fahrenheit and Celsius temperatures

Many measurements in the United States are made in metric units. A drink may come in

\text{2-liter}

bottles, calcium may come in

\text{500-mg}

capsules, and we may run a

\text{5-K}

race. To work easily in both systems, we need to be able to convert between the two systems. The reference table below shows some of the most common conversions.

Conversion Factors Between U.S. and Metric Systems
Length	Weight	Volume
$1$ in = $2.54$ cm $1$ ft = $0.305$ m $1$ yd = $0.914$ m $1$ mi = $1.61$ km $1$ m = $3.28$ ft	$1$ lb = $0.45$ kg $1$ oz = $28$ g $1$ kg = $2.2$ lb	$1$ qt = $0.95$ L $1$ fl oz = $30$ mL $1$ L = $1.06$ qt

We make conversions between the systems just as we do within the systems—by multiplying by unit conversion factors.

example

Lee’s water bottle holds

500

mL of water. How many fluid ounces are in the bottle? Round to the nearest tenth of an ounce. Solution

	$500\text{mL}$
Multiply by a unit conversion factor relating mL and ounces.	$500\text{mL}\cdot\Large\frac{1\text{fl oz}}{30\text{mL}}$
Simplify.	$\Large\frac{500\text{fl oz}}{30}$
Divide.	$16.7\text{fl. oz.}$
	The water bottle holds $16.7$ fluid ounces.

try it

[ohm_question]146876[/ohm_question] [ohm_question]146877[/ohm_question]

The conversion factors in the reference table are not exact, but the approximations they give are close enough for everyday purposes. In the last example, we rounded the number of fluid ounces to the nearest tenth.

Exercises

Soleil lives in Minnesota but often travels in Canada for work. While driving on a Canadian highway, she passes a sign that says the next rest stop is in

100

kilometers. How many miles until the next rest stop? Round your answer to the nearest mile.

Answer: Solution

	$\text{100 kilometers}$
Multiply by a unit conversion factor relating kilometers and miles.	$100\text{kilometers}\cdot \Large\frac{1\text{mile}}{1.61\text{kilometers}}$ $100\cdot \Large\frac{1\text{mi}}{1.61\text{km}}$
Simplify.	$\Large\frac{100\text{mi}}{1.61}$
Divide.	$62 \text{mi}$
	It is about $62$ miles to the next rest stop.

TRY IT

[ohm_question]146878[/ohm_question] [ohm_question]146879[/ohm_question]

Convert Between Fahrenheit and Celsius Temperatures

Have you ever been in a foreign country and heard the weather forecast? If the forecast is for

22^\circ C

. What does that mean? The U.S. and metric systems use different scales to measure temperature. The U.S. system uses degrees Fahrenheit, written

^\circ F

. The metric system uses degrees Celsius, written

^\circ C

. The image below shows the relationship between the two systems. A temperature of

37^\circ C

is equivalent to

98.6^\circ F

On the left side of the figure is a thermometer marked in degrees Celsius. The bottom of the thermometer begins with negative 20 degrees Celsius and ranges up to 100 degrees Celsius. There are tick marks on the thermometer every 5 degrees with every 10 degrees labeled. On the right side is a thermometer marked in degrees Fahrenheit. The bottom of the thermometer begins with negative 10 degrees Fahrenheit and ranges up to 212 degrees Fahrenheit. There are tick marks on the thermometer every 2 degrees with every 10 degrees labeled. Between the thermometers there is an arrow pointing on the left to 0 degrees Celsius and on the right to 32 degrees Fahrenheit. This is the temperature at which water freezes. Another arrow points on the left to 37 degrees Celsius and on the right to 98.6 degrees Fahrenheit. This is normal body temperature. A third arrow points on the left to 100 degrees Celsius and on the right to 212 degrees Fahrenheit. This is the temperature at which water boils.

If we know the temperature in one system, we can use a formula to convert it to the other system.

Temperature Conversion

To convert from Fahrenheit temperature,

\text{F}

, to Celsius temperature,

\text{C}

, use the formula

C=\Large\frac{5}{9}\normalsize\left(F - 32\right)

To convert from Celsius temperature,

\text{C}

, to Fahrenheit temperature,

\text{F}

, use the formula

F=\Large\frac{9}{5}\normalsize C+32

Exercises

Convert

50^\circ F

into degrees Celsius.

Answer: Solution We will substitute $50^\circ F$ into the formula to find $\text{C}$ .

Use the formula for converting °F to °C	$C=\Large\frac{5}{9}\normalsize\left(F - 32\right)$
Substitute $\color{red}{50}$ for °F.	$C=\Large\frac{5}{9}\normalsize(\color{red}{50}-32)$
Simplify in parentheses.	$C=\Large\frac{5}{9}\normalsize\left(18\right)$
Multiply.	$C=10$
	A temperature of $50°F$ is equivalent to $10°C$ .

TRY IT

[ohm_question]146880[/ohm_question]

example

The weather forecast for Paris predicts a high of

20^\circ C

Convert the temperature into degrees Fahrenheit.

Answer: Solution We will substitute $20^\circ C$ into the formula to find $F$ .

Use the formula for converting °F to °C	$F=\Large\frac{9}{5}\normalsize C+32$
Substitute $\color{red}{20}$ for °C.	$F=\Large\frac{9}{5}\normalsize(\color{red}{20})+32$
Multiply.	$F=36+32$
Add.	$F=68$
	So $20°C$ is equivalent to $68°F$

Converting Between U.S. and Metric Systems of Measurement

Learning Outcomes

example

try it

Exercises

TRY IT

Convert Between Fahrenheit and Celsius Temperatures

Temperature Conversion

Exercises

TRY IT

example

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Contribute!

Licenses & Attributions

CC licensed content, Original

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Guias de estudo > ALGEBRA / TRIG I

Converting Between U.S. and Metric Systems of Measurement

Learning Outcomes

example

try it

Exercises

TRY IT

Convert Between Fahrenheit and Celsius Temperatures

Temperature Conversion

Exercises

TRY IT

example

try it

Contribute!

Licenses & Attributions

CC licensed content, Original

CC licensed content, Specific attribution