Scientific Notation/Examples/Division/Powers of 10

Example of Division using Scientific Notation

$\dfrac {10^6} {10^4} = 10^2$

Proof

\(\ds \dfrac {10^6} {10^4}\)

\(=\)

\(\ds \paren {10^6} \paren {10^{-4} }\)

Negative Power

\(\ds \)

\(=\)

\(\ds 10^{6 - 4}\)

Product of Powers

\(\ds \)

\(=\)

\(\ds 10^2\)

That is:

\(\ds \dfrac {10^6} {10^4}\)

\(=\)

\(\ds \dfrac {1 \, 000 \, 000} {10 \, 000}\)

Definition of Scientific Notation

\(\ds \)

\(=\)

\(\ds 100\)

\(\ds \)

\(=\)

\(\ds 10^2\)

Definition of Scientific Notation

$\blacksquare$

Sources

• 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Scientific Notation: Example 1.