Scientific Notation/Examples/Multiplication/Arbitrary Example
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Example of Multiplication using Scientific Notation
- $\paren {4 \, 000 \, 000} \paren {0 \cdotp 000 \, 000 \, 000 \, 2} = 0 \cdotp 000 \, 8$
Proof
| \(\ds \paren {4 \, 000 \, 000} \paren {0 \cdotp 000 \, 000 \, 000 \, 2}\) | \(=\) | \(\ds \paren {4 \times 10^6} \paren {2 \times 10^{10} }\) | Definition of Scientific Notation | |||||||||||
| \(\ds \) | \(=\) | \(\ds 4 \times 2 \times 10^{6 - 10}\) | Product of Powers | |||||||||||
| \(\ds \) | \(=\) | \(\ds 8 \times 10^{-4}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 12 \, 000\) | 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 2.