Solved on Mar 29, 2024

Given dosage strength is $0.2 \mathrm{mg}$ in $1.5 \mathrm{mL}$ . Determine the volume needed to prepare $0.19 \mathrm{mg}$ dosage.
The available dosage strength is $0.2 \mathrm{mg}$ in $\mathrm{mL}$ . The goal is to determine how many $\mathrm{mL}$ will be needed to prepare a dosage of $0.19 \mathrm{mg}$ . The units are conversion ratio $\frac{\mathrm{mg}}{\mathrm{mL}}$ .
$\mathrm{mL}=\frac{\mathrm{mg}}{\frac{\mathrm{mg}}{\mathrm{mL}}} \times 0.19 \mathrm{mg}$

STEP 1

1. DA stands for Dimensional Analysis, which is a method to convert one unit of measure to another using a conversion factor.
2. The conversion factor is the ratio of the dosage strength available.
3. The dosage required is given in milligrams (mg) and needs to be converted to milliliters (mL) using the available dosage strength.

STEP 2

1. Identify the conversion factor from the available dosage strength.
2. Set up the equation for Dimensional Analysis using the conversion factor.
3. Solve the equation to find the required dosage in mL.
4. Round the answer to the nearest tenth.

STEP 3

Identify the conversion factor from the available dosage strength, which is $0.2 \mathrm{mg}$ in $1.5 \mathrm{mL}$ .
$\text{Conversion factor} = \frac{1.5 \mathrm{mL}}{0.2 \mathrm{mg}}$

STEP 4

Set up the equation for Dimensional Analysis using the conversion factor to calculate the dosage in mL for $0.19 \mathrm{mg}$ .
$\mathrm{mL} = \frac{1.5 \mathrm{mL}}{0.2 \mathrm{mg}} \times 0.19 \mathrm{mg}$

STEP 5

Solve the equation to find the required dosage in mL.
$\mathrm{mL} = \frac{1.5 \mathrm{mL}}{0.2 \mathrm{mg}} \times 0.19 \mathrm{mg}$

STEP 6

Perform the multiplication to calculate the dosage in mL.
$\mathrm{mL} = \frac{1.5}{0.2} \times 0.19$

STEP 7

Calculate the numerical value.
$\mathrm{mL} = 7.5 \times 0.19$

STEP 8

Complete the calculation.
$\mathrm{mL} = 1.425$

STEP 9

Round the answer to the nearest tenth.
$\mathrm{mL} \approx 1.4$
The required dosage is approximately $1.4 \mathrm{mL}$ .

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STEP 1

STEP 2

1. Identify the conversion factor from the available dosage strength.
2. Set up the equation for Dimensional Analysis using the conversion factor.
3. Solve the equation to find the required dosage in mL.
4. Round the answer to the nearest tenth.

STEP 3

Identify the conversion factor from the available dosage strength, which is $0.2 \mathrm{mg}$ in $1.5 \mathrm{mL}$ .
$\text{Conversion factor} = \frac{1.5 \mathrm{mL}}{0.2 \mathrm{mg}}$

STEP 4

Set up the equation for Dimensional Analysis using the conversion factor to calculate the dosage in mL for $0.19 \mathrm{mg}$ .
$\mathrm{mL} = \frac{1.5 \mathrm{mL}}{0.2 \mathrm{mg}} \times 0.19 \mathrm{mg}$

STEP 5

Solve the equation to find the required dosage in mL.
$\mathrm{mL} = \frac{1.5 \mathrm{mL}}{0.2 \mathrm{mg}} \times 0.19 \mathrm{mg}$

STEP 6

Perform the multiplication to calculate the dosage in mL.
$\mathrm{mL} = \frac{1.5}{0.2} \times 0.19$

STEP 7

Calculate the numerical value.
$\mathrm{mL} = 7.5 \times 0.19$

STEP 8

Complete the calculation.
$\mathrm{mL} = 1.425$

STEP 9

Round the answer to the nearest tenth.
$\mathrm{mL} \approx 1.4$
The required dosage is approximately $1.4 \mathrm{mL}$ .

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STEP 1

STEP 2

1. Identify the conversion factor from the available dosage strength.2. Set up the equation for Dimensional Analysis using the conversion factor.3. Solve the equation to find the required dosage in mL.4. Round the answer to the nearest tenth.

STEP 3

Identify the conversion factor from the available dosage strength, which is 0.2mg0.2 \mathrm{mg}0.2mg in 1.5mL1.5 \mathrm{mL}1.5mL.Conversion factor=1.5mL0.2mg \text{Conversion factor} = \frac{1.5 \mathrm{mL}}{0.2 \mathrm{mg}} Conversion factor=0.2mg1.5mL​

STEP 4

Set up the equation for Dimensional Analysis using the conversion factor to calculate the dosage in mL for 0.19mg0.19 \mathrm{mg}0.19mg.mL=1.5mL0.2mg×0.19mg \mathrm{mL} = \frac{1.5 \mathrm{mL}}{0.2 \mathrm{mg}} \times 0.19 \mathrm{mg} mL=0.2mg1.5mL​×0.19mg

STEP 5

Solve the equation to find the required dosage in mL.mL=1.5mL0.2mg×0.19mg \mathrm{mL} = \frac{1.5 \mathrm{mL}}{0.2 \mathrm{mg}} \times 0.19 \mathrm{mg} mL=0.2mg1.5mL​×0.19mg

STEP 6

Perform the multiplication to calculate the dosage in mL.mL=1.50.2×0.19 \mathrm{mL} = \frac{1.5}{0.2} \times 0.19 mL=0.21.5​×0.19

STEP 7

Calculate the numerical value.mL=7.5×0.19 \mathrm{mL} = 7.5 \times 0.19 mL=7.5×0.19

STEP 8

Complete the calculation.mL=1.425 \mathrm{mL} = 1.425 mL=1.425

STEP 9

Round the answer to the nearest tenth.mL≈1.4 \mathrm{mL} \approx 1.4 mL≈1.4The required dosage is approximately 1.4mL1.4 \mathrm{mL}1.4mL.

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1. Identify the conversion factor from the available dosage strength.
2. Set up the equation for Dimensional Analysis using the conversion factor.
3. Solve the equation to find the required dosage in mL.
4. Round the answer to the nearest tenth.

Identify the conversion factor from the available dosage strength, which is $0.2 \mathrm{mg}$ in $1.5 \mathrm{mL}$ .
$\text{Conversion factor} = \frac{1.5 \mathrm{mL}}{0.2 \mathrm{mg}}$

Set up the equation for Dimensional Analysis using the conversion factor to calculate the dosage in mL for $0.19 \mathrm{mg}$ .
$\mathrm{mL} = \frac{1.5 \mathrm{mL}}{0.2 \mathrm{mg}} \times 0.19 \mathrm{mg}$

Solve the equation to find the required dosage in mL.
$\mathrm{mL} = \frac{1.5 \mathrm{mL}}{0.2 \mathrm{mg}} \times 0.19 \mathrm{mg}$

Perform the multiplication to calculate the dosage in mL.
$\mathrm{mL} = \frac{1.5}{0.2} \times 0.19$

Calculate the numerical value.
$\mathrm{mL} = 7.5 \times 0.19$

Complete the calculation.
$\mathrm{mL} = 1.425$

Round the answer to the nearest tenth.
$\mathrm{mL} \approx 1.4$
The required dosage is approximately $1.4 \mathrm{mL}$ .