1. Lesson Presentation

2. Learn to evaluate negative exponents and use them to write scientific notation and in standard form.

3. When a natural number has a positive exponent, the value of the power is greater than or equal to 1. When a natural number has a negative exponent, the value of the power is less than or equal to 1. When any natural number has a zero exponent, the value of the power is equal to 1.

4. Additional Example 1: Evaluating Negative Exponents
Evaluate 10–7.
Write the fraction with a positive exponent in the denominator.
Evaluate the power.
Write the decimal form.

5. Check It Out: Example 1
Evaluate 10–2.
Write the fraction with a positive exponent in the denominator.
Evaluate the power.
Write the decimal form.

6. Additional Example 2: Writing Small Numbers in Scientific Notation
Write in scientific notation.
Move the decimal point 5 places to the right. =
Write as a product of two factors.
= 3.9 
Write the exponential form. Since the decimal point was moved 5 places, the exponent is 5.
= 3.9  105

7. Check It Out: Example 2
Write in scientific notation.
Move the decimal point 4 places to the right. =
Write as a product of two factors.
= 2.2 
Write the exponential form. Since the decimal point was moved 4 places, the exponent is 4.
= 2.2  104

8. Additional Example 3: Writing Small Numbers in Standard Form
Write 7.8  10–4 in scientific notation.
Since the exponent is –4, move the decimal point 4 places to the left.
7.8  10–4 = =

9. Check It Out: Example 3
Write 3.3  10–3 in scientific notation.
Since the exponent is –3, move the decimal point 3 places to the left.
3.3  10–3 = =

10. Additional Example 4A: Comparing Numbers Using Scientific Notation
Compare. Write <, >, or =.
5.2  10–6 ___ 8.1  10–14
Compare the powers of ten.
10–6 > 10–14
5.2  10–6 > 8.1  10–14

11. Additional Example 4B: Comparing Numbers Using Scientific Notation
Compare. Write <, >, or =.
2.9  10–7 ___ 5.3  10–7
Compare the powers of ten.
10–7 = 10–7
Since the powers of ten are equal, compare the decimals.
2 is less than 5.
2.9 < 5.3
2.9  10–7 < 5.3  10–7

12. Check It Out: Example 4
Compare. Write <, >, or =.
5.2  10–5 ___ 4.3  10–5
Compare the powers of ten.
10–5 = 10–5
Since the powers of ten are equal, compare the decimals.
5 is greater than 4.
5.2 > 4.3
5.2  10–5 > 4.3  10–5