Question

for use after lesson 10.5
tell whether the number is written in scientific notation. explain.

1. 14×10^8
2. 2.6×10^12
3. 4.79×10^(-8)
4. 3.99×10^16
5. 0.15×10^22
6. 6×10^3

Explanation:

Step1: Recall scientific - notation rule

Scientific notation is of the form $a\times10^{n}$, where $1\leq|a|\lt10$ and $n$ is an integer.

Step2: Analyze 1. $14\times10^{8}$

Since $a = 14$ and $14\geq10$, it is not in scientific notation.

Step3: Analyze 2. $2.6\times10^{12}$

Here, $1\leq2.6\lt10$ and $n = 12$ is an integer, so it is in scientific notation.

Step4: Analyze 3. $4.79\times10^{-8}$

Since $1\leq4.79\lt10$ and $n=-8$ is an integer, it is in scientific notation.

Step5: Analyze 4. $3.99\times10^{16}$

As $1\leq3.99\lt10$ and $n = 16$ is an integer, it is in scientific notation.

Step6: Analyze 5. $0.15\times10^{22}$

Since $a = 0.15$ and $0.15\lt1$, it is not in scientific notation.

Step7: Analyze 6. $6\times10^{3}$

Since $1\leq6\lt10$ and $n = 3$ is an integer, it is in scientific notation.

Answer:

1. Not in scientific notation. Explanation: The coefficient 14 is greater than or equal to 10.
2. In scientific notation. Explanation: The coefficient 2.6 is between 1 and 10, and the exponent 12 is an integer.
3. In scientific notation. Explanation: The coefficient 4.79 is between 1 and 10, and the exponent - 8 is an integer.
4. In scientific notation. Explanation: The coefficient 3.99 is between 1 and 10, and the exponent 16 is an integer.
5. Not in scientific notation. Explanation: The coefficient 0.15 is less than 1.
6. In scientific notation. Explanation: The coefficient 6 is between 1 and 10, and the exponent 3 is an integer.