Convert assay ton to gamma

Learn how to convert 1 assay ton to gamma step by step.

Calculation Breakdown

Set up the equation

1.0 (a s s a y t o n) = x (g a m m a)

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

(k i l o g r a m)

Left side: 1.0 (a s s a y t o n) = \frac{49.0}{1.5 \times 10^{3}} (k i l o g r a m) = \frac{49.0}{1.5 \times 10^{3}} (k g)

Right side: 1.0 (g a m m a) = 10^{- 9} (k i l o g r a m) = 10^{- 9} (k g)

Insert known values into the conversion equation to determine

x

1.0 (a s s a y t o n) = x (g a m m a)

Insert known values =>

1.0 \times \frac{49.0}{1.5 \times 10^{3}} \times (k i l o g r a m) = x \times 10^{- 9} \times (k i l o g r a m)

Or

1.0 \cdot \frac{49.0}{1.5 \times 10^{3}} \cdot (k g) = x \cdot 10^{- 9} \cdot (k g)

Cancel SI units

1.0 \times \frac{49.0}{1.5 \times 10^{3}} \cdot (k g) = x \times 10^{- 9} \times (k g)

Conversion Equation

\frac{49.0}{1.5 \times 10^{3}} = x \times 10^{- 9}

Switch sides

x \times 10^{- 9} = \frac{49.0}{1.5 \times 10^{3}}

Isolate

x

Multiply both sides by

(\frac{1.0}{10^{- 9}})

x \times 10^{- 9} \times \frac{1.0}{10^{- 9}} = \frac{49.0}{1.5 \times 10^{3}} \times \frac{1.0}{10^{- 9}}

Cancel

x \times 10^{- 9} \times \frac{1.0}{10^{- 9}} = \frac{49.0 \times 1.0}{1.5 \times 10^{3} \times {10^{- 9}}^{10^{- 6}}}

Simplify

x = \frac{49.0}{1.5 \times 10^{- 6}}

Rewrite equation

\frac{1.0}{10^{- 6}} can be rewritten to 10^{6}

Rewrite

x = \frac{10^{6} \times 49.0}{1.5}

Solve

x

x \approx 32666666.667 \approx 3.2667 \times 10^{7}

Conversion Equation

1.0 (a s s a y t o n) \approx 3.2667 \times 10^{7} (g a m m a)

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