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I-04: Dimensional analysis and metric conversions

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Module I-04 · Recommended before: Before moles and all solution calculations

Dimensional analysis and metric conversions

A conversion factor is a ratio equal to one. Set factors so unwanted units cancel. This method prevents hidden unit errors.

Learn the method

1 g = 1000 mg; 1 L = 1000 mL

  1. Write the given number with units.
  2. Multiply by a fraction with a valid equality.
  3. Place the unit you want to eliminate opposite itself.
  4. Cancel units and compute.
  5. Estimate the order of magnitude.

Common mistake: Do not multiply by 1000 when converting milligrams to grams.

Worked example

Problem: Convert 250 mg to grams.

Step-by-step solution: 250 mg × (1 g / 1000 mg) = 0.250 g; milligrams cancel.

Check the units and whether the answer is reasonable before continuing.

More applications of this mathematics

Try each extension before expanding its solution.

Multistep units

Convert 0.250 L into µL: 0.250 L × (1000 mL/L) × (1000 µL/mL) = 2.50 × 10⁵ µL.

Compound unit conversion

Convert 5.00 g/L to mg/mL: (5.00 g/L)×(1000 mg/g)×(1 L/1000 mL)=5.00 mg/mL.

Independent practice — five questions

Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. Convert 8 mg to grams.
Hint for question 1

One gram is one thousand milligrams.

Question 2. Convert 1500 mg to grams.
Hint for question 2

One gram is one thousand milligrams.

Question 3. Convert 250 mg to grams.
Hint for question 3

One gram is one thousand milligrams.

Question 4. Convert 420 mg to grams.
Hint for question 4

One gram is one thousand milligrams.

Question 5. Convert 999 mg to grams.
Hint for question 5

One gram is one thousand milligrams.

Supporting reference

OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original.

W3C WCAG 2.2 accessibility guidance.

Applied practice: Multistep unit conversions

Additional ungraded questions help you practice other calculations in this topic. Work each problem before opening its solution; your scored quiz and progress are not changed.

  1. Challenge 1. Convert a density of 0.450 g/cm³ to kg/m³.

    Show worked solution for challenge 1

    1 g/cm³ = 1000 kg/m³, so (0.450)(1000) = 450 kg/m³ (three significant figures).

  2. Challenge 2. Convert 2.50 L to cubic centimeters.

    Show worked solution for challenge 2

    1 L = 1000 cm³ exactly. Therefore 2.50 L × (1000 cm³/L) = 2.50 × 10³ cm³.

IntoChemistry original instructional content, 2026. Formative feedback is not an official course grade. Sources are linked for independent reading. Accessibility testing with your institution and assistive technology is still recommended.