Write each number in scientific notation.

1. 14,700

2. 0.00083

3. 760,000,000

4. 0.038

5. 0.38

6. 3.8

7. 3,800,000,000,000

8. 0.0000000009

Elena is going to write the number 0.0000025 in scientific notation. She writes “\(2.5 \times 10^{?}\)” but isn’t sure what to write for the exponent. Explain how Elena can decide which power of 10 to use.

The following numbers are all written in scientific notation. Write the value of each expression.

1. \(8.5 \times 10^6\)

2. \(4.54 \times 10^{10}\)

3. \(9.03 \times 10^2\)

4. \(3.714 \times 10^{\text-5}\)

5. \(5.82 \times 10^{\text-8}\)

Here is the graph for one equation in a system of equations.

1. Write a second equation for the system so it has infinitely many solutions.
2. Write a second equation whose graph goes through \((0,2)\) so that the system has no solutions.
3. Write a second equation whose graph goes through \((2,2)\) so that the system has one solution at \((4,3)\).

Write each expression using a single exponent:

1. \(\frac{5^3}{5^7}\)
2. \(5^3\boldcdot5^3\boldcdot5^2\)
3. \((5^3)^7\)
4. \(5\boldcdot5^0\boldcdot5^1\)