Convert deca to giga
Learn how to convert
1
deca to
giga
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(deca\right)={\color{rgb(20,165,174)} x}\left(giga\right)\)
Define the prefix value(s)
\(The \text{ } value \text{ } of \text{ } deca \text{ } is \text{ } 10.0\)
\(The \text{ } value \text{ } of \text{ } giga \text{ } is \text{ } 10^{9}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(deca\right)={\color{rgb(20,165,174)} x}\left(giga\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10.0} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{9}}}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10.0} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{9}}\)
\(\text{Conversion Equation}\)
\(10.0 = {\color{rgb(20,165,174)} x} \times 10^{9}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancel{10.0}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancelto{10^{8}}{10^{9}}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times 10^{8}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10^{8} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10^{8}}\right)\)
\({\color{rgb(20,165,174)} x} \times 10^{8} \times \dfrac{1.0}{10^{8}} = \times \dfrac{1.0}{10^{8}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{8}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{8}}}} = \dfrac{1.0}{10^{8}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{10^{8}}\)
Rewrite equation
\(\dfrac{1.0}{10^{8}}\text{ can be rewritten to }10^{-8}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = 10^{-8}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 10^{-8}\)
\(\text{Conversion Equation}\)
\(1.0\left(deca\right) = {\color{rgb(20,165,174)} 10^{-8}}\left(giga\right)\)
