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Decide if the numbers are written in scientific notation or not. Use Definition 6.3.3.

The number $7 \times 10^{1.9}$ is .

The number $2.6 \times 10^{-31}$ is .

The number $10 \times 7^4$ is .

The number $0.93 \times 10^{3}$ is .

The number $4.2 \times 10^0$ is .

The number $12.5 \times 10^{-6}$ is .

Solution

The number $7 \times 10^{1.9}$ is not in scientific notation. The exponent on the 10 is required to be an integer and $1.9$ is not.

The number $2.6 \times 10^{-31}$ is in scientific notation.

The number $10 \times 7^4$ is not in scientific notation. The base must be $10\text{,}$ not $7\text{.}$

The number $0.93 \times 10^{3}$ is not in scientific notation. The coefficient of the 10 must be between $1$ (inclusive) and $10\text{.}$

The number $4.2 \times 10^0$ is in scientific notation.

The number $12.5 \times 10^{-6}$ is not in scientific notation. The coefficient of the 10 must be between $1$ (inclusive) and $10\text{.}$