Solve multi-step unit-conversion problems

Measurement quantities are preserved while their numerical representations change through known equivalences among units of length, mass, capacity, and time. Learners coordinate successive conversions, including through an intermediate unit, and use multiplication or division with whole numbers, fractions, and decimals while tracking units to interpret the final quantity and avoid treating conversion as an additive change. The scope excludes compound-unit conversions such as speed or density and generalized dimensional analysis.

Detailed Explanation: Solve multi-step unit-conversion problems

To solve a multi-step unit conversion:

Write the given amount and unit.
Convert to an intermediate unit.
Convert from the intermediate unit to the final unit.
Multiply or divide using the conversion facts.
Check that the final unit is the one requested.

Example

Convert $2.4$ kilograms to milligrams.

We need to pass through grams:

$1$ kilogram $= 1{,}000$ grams
$1$ gram $= 1{,}000$ milligrams

Step 1: Convert kilograms to grams.

Since kilograms are larger than grams, multiply by $1{,}000$ :

2.4\text{ kg} \times 1{,}000 = 2{,}400\text{ g}

Step 2: Convert grams to milligrams.

Again, multiply by $1{,}000$ :

2{,}400\text{ g} \times 1{,}000 = 2{,}400{,}000\text{ mg}

Therefore,

\boxed{2.4\text{ kg} = 2{,}400{,}000\text{ mg}}

The amount of mass did not change; only its numerical representation changed. Since the final unit is milligrams, the answer is complete.

Learn by doing: Solve multi-step unit-conversion problems

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Measurement Conversion - Metric Length Units (All) with Decimals - Small to Large

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