Convert pennyweight to carat

Learn how to convert 1 pennyweight to carat step by step.

Calculation Breakdown

Set up the equation
1.0(pennyweight)=x(carat)
Define the base values of the selected units in relation to the SI unit (kilogram)
Left side: 1.0 (pennyweight)=1.55517384×103(kilogram)=1.55517384×103(kg)
Right side: 1.0 (carat)=2.0×104(kilogram)=2.0×104(kg)
Insert known values into the conversion equation to determine x
1.0(pennyweight)=x(carat)
Insert known values =>
1.0×1.55517384×103×(kilogram)=x×2.0×104×(kilogram)
Or
1.01.55517384×103(kg)=x2.0×104(kg)
Cancel SI units
1.0×1.55517384×103(kg)=x×2.0×104×(kg)
Conversion Equation
1.55517384×103=x×2.0×104
Cancel factors on both sides
Cancel factors
1.55517384×103=x×2.0×104101
Simplify
1.55517384=x×2.0×101
Switch sides
x×2.0×101=1.55517384
Isolate x
Multiply both sides by (1.02.0×101)
x×2.0×101×1.02.0×101=1.55517384×1.02.0×101
Cancel
x×2.0×101×1.02.0×101=1.55517384×1.02.0×101
Simplify
x=1.555173842.0×101
Rewrite equation
1.0101 can be rewritten to 10
Rewrite
x=10.0×1.555173842.0
Solve x
x=7.77586927.7759
Conversion Equation
1.0(pennyweight)7.7759(carat)

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