Convert gallon to cup

Learn how to convert 1 gallon to cup step by step.

Calculation Breakdown

Set up the equation

1.0 (g a l l o n) = x (c u p)

Define the base values of the selected units in relation to the SI unit

(c u b i c m e t e r)

Left side: 1.0 (g a l l o n) = 4.621152048 \times 10^{- 3} (c u b i c m e t e r) = 4.621152048 \times 10^{- 3} (m^{3})

Right side: 1.0 (c u p) = 2.273045 \times 10^{- 4} (c u b i c m e t e r) = 2.273045 \times 10^{- 4} (m^{3})

Insert known values into the conversion equation to determine

x

1.0 (g a l l o n) = x (c u p)

Insert known values =>

1.0 \times 4.621152048 \times 10^{- 3} \times (c u b i c m e t e r) = x \times 2.273045 \times 10^{- 4} \times (c u b i c m e t e r)

Or

1.0 \cdot 4.621152048 \times 10^{- 3} \cdot (m^{3}) = x \cdot 2.273045 \times 10^{- 4} \cdot (m^{3})

Cancel SI units

1.0 \times 4.621152048 \times 10^{- 3} \cdot (m^{3}) = x \times 2.273045 \times 10^{- 4} \times (m^{3})

Conversion Equation

4.621152048 \times 10^{- 3} = x \times 2.273045 \times 10^{- 4}

Cancel factors on both sides

Cancel factors

4.621152048 \times 10^{- 3} = x \times 2.273045 \times {10^{- 4}}^{10^{- 1}}

Simplify

4.621152048 = x \times 2.273045 \times 10^{- 1}

Switch sides

x \times 2.273045 \times 10^{- 1} = 4.621152048

Isolate

x

Multiply both sides by

(\frac{1.0}{2.273045 \times 10^{- 1}})

x \times 2.273045 \times 10^{- 1} \times \frac{1.0}{2.273045 \times 10^{- 1}} = 4.621152048 \times \frac{1.0}{2.273045 \times 10^{- 1}}

Cancel

x \times 2.273045 \times 10^{- 1} \times \frac{1.0}{2.273045 \times 10^{- 1}} = 4.621152048 \times \frac{1.0}{2.273045 \times 10^{- 1}}

Simplify

x = \frac{4.621152048}{2.273045 \times 10^{- 1}}

Rewrite equation

\frac{1.0}{10^{- 1}} can be rewritten to 10

Rewrite

x = \frac{10.0 \times 4.621152048}{2.273045}

Solve

x

x \approx 20.330226845 \approx 20.3302

Conversion Equation

1.0 (g a l l o n) \approx 20.3302 (c u p)

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