Convert digit to douzième
Learn how to convert
1
digit to
douzième
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(digit\right)={\color{rgb(20,165,174)} x}\left(douzième\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(digit\right) = {\color{rgb(89,182,91)} 1.9 \times 10^{-2}\left(meter\right)} = {\color{rgb(89,182,91)} 1.9 \times 10^{-2}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(douzième\right) = {\color{rgb(125,164,120)} 1.88 \times 10^{-4}\left(meter\right)} = {\color{rgb(125,164,120)} 1.88 \times 10^{-4}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(digit\right)={\color{rgb(20,165,174)} x}\left(douzième\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.9 \times 10^{-2}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.88 \times 10^{-4}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.9 \times 10^{-2}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.88 \times 10^{-4}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.9 \times 10^{-2}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.88 \times 10^{-4}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(1.9 \times 10^{-2} = {\color{rgb(20,165,174)} x} \times 1.88 \times 10^{-4}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(1.9 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}} = {\color{rgb(20,165,174)} x} \times 1.88 \times {\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-4}}}\)
\(\text{Simplify}\)
\(1.9 = {\color{rgb(20,165,174)} x} \times 1.88 \times 10^{-2}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.88 \times 10^{-2} = 1.9\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.88 \times 10^{-2}}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.88 \times 10^{-2} \times \dfrac{1.0}{1.88 \times 10^{-2}} = 1.9 \times \dfrac{1.0}{1.88 \times 10^{-2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.88}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.88}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}} = 1.9 \times \dfrac{1.0}{1.88 \times 10^{-2}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.9}{1.88 \times 10^{-2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{2} \times 1.9}{1.88}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx101.06382979\approx1.0106 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(digit\right)\approx{\color{rgb(20,165,174)} 1.0106 \times 10^{2}}\left(douzième\right)\)
