Convert mach to mile / hour

Learn how to convert 1 mach to mile / hour step by step.

Calculation Breakdown

Set up the equation

1.0 (m a c h) = x (\frac{m i l e}{h o u r})

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

(\frac{m e t e r}{s e c o n d})

Left side: 1.0 (m a c h) = 331.0 (\frac{m e t e r}{s e c o n d}) = 331.0 (\frac{m}{s})

Right side: 1.0 (\frac{m i l e}{h o u r}) = \frac{1609.344}{3.6 \times 10^{3}} (\frac{m e t e r}{s e c o n d}) = \frac{1609.344}{3.6 \times 10^{3}} (\frac{m}{s})

Insert known values into the conversion equation to determine

x

1.0 (m a c h) = x (\frac{m i l e}{h o u r})

Insert known values =>

1.0 \times 331.0 \times (\frac{m e t e r}{s e c o n d}) = x \times \frac{1609.344}{3.6 \times 10^{3}} \times (\frac{m e t e r}{s e c o n d})

Or

1.0 \cdot 331.0 \cdot (\frac{m}{s}) = x \cdot \frac{1609.344}{3.6 \times 10^{3}} \cdot (\frac{m}{s})

Cancel SI units

1.0 \times 331.0 \cdot (\frac{m}{s}) = x \times \frac{1609.344}{3.6 \times 10^{3}} \times (\frac{m}{s})

Conversion Equation

331.0 = x \times \frac{1609.344}{3.6 \times 10^{3}}

Switch sides

x \times \frac{1609.344}{3.6 \times 10^{3}} = 331.0

Isolate

x

Multiply both sides by

(\frac{3.6 \times 10^{3}}{1609.344})

x \times \frac{1609.344}{3.6 \times 10^{3}} \times \frac{3.6 \times 10^{3}}{1609.344} = 331.0 \times \frac{3.6 \times 10^{3}}{1609.344}

Cancel

x \times \frac{1609.344 \times 3.6 \times 10^{3}}{3.6 \times 10^{3} \times 1609.344} = 331.0 \times \frac{3.6 \times 10^{3}}{1609.344}

Simplify

x = \frac{331.0 \times 3.6 \times 10^{3}}{1609.344}

Solve

x

x \approx 740.42591267 \approx 7.4043 \times 10^{2}

Conversion Equation

1.0 (m a c h) \approx 7.4043 \times 10^{2} (\frac{m i l e}{h o u r})

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