QuestionConvert $1.000 \times 10^{3} \mathrm{~cm}^{3}$ of water to gallons using $1 \mathrm{~cm}^{3}=1 \mathrm{~mL}$ and $1 \mathrm{~L}=0.264$ gallons.

Studdy Solution

STEP 1

Assumptions1. The volume of water is $1.000 \times10^{3} \mathrm{~cm}^{3}$ . The conversion factor from cubic centimeters to milliliters is $1 \mathrm{~cm}^{3}=1 \mathrm{~m}$
3. The conversion factor from liters to gallons is $1 \mathrm{~}=0.264$ gallons4. All unit conversions are treated as exact numbers, meaning they have infinite significant figures.

STEP 2

First, we need to convert the volume of water from cubic centimeters to milliliters using the conversion factor.
Volume_{m} = Volume_{cm^} \times Conversion\, factor_{cm^\, to\, mL}

STEP 3

Now, plug in the given values for the volume and the conversion factor to calculate the volume in milliliters.
$Volume_{m} =1.000 \times10^{3} \mathrm{~cm}^{3} \times1 \mathrm{~m/cm}^{3}$

STEP 4

Calculate the volume in milliliters.
$Volume_{m} =1.000 \times10^{3} \mathrm{~m}$

STEP 5

Next, we need to convert the volume from milliliters to liters. Since there are1000 milliliters in a liter, we can do this by dividing the volume in milliliters by1000.
$Volume_{} = Volume_{m} /1000$

STEP 6

Plug in the value for the volume in milliliters to calculate the volume in liters.
$Volume_{} =1.000 \times10^{3} \mathrm{~m} /1000$

STEP 7

Calculate the volume in liters.
$Volume_{} =1.000 \mathrm{~}$

STEP 8

Finally, we need to convert the volume from liters to gallons using the conversion factor.
$Volume_{gallons} = Volume_{} \times Conversion\, factor_{\, to\, gallons}$

STEP 9

Plug in the values for the volume in liters and the conversion factor to calculate the volume in gallons.
$Volume_{gallons} =.000 \mathrm{~} \times.264 \mathrm{~gallons/L}$

STEP 10

Calculate the volume in gallons.
$Volume_{gallons} =.000 \times0.264 \mathrm{~gallons} =0.264 \mathrm{~gallons}$ You have0.264 gallons of water.

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