Lesson Presentation

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

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.

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.

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.

Additional Example 2: Writing Small Numbers in Scientific Notation Write 0.000039 in scientific notation. Move the decimal point 5 places to the right. 0.000039 = 0.000039 Write as a product of two factors. = 3.9  0.00001 Write the exponential form. Since the decimal point was moved 5 places, the exponent is 5. = 3.9  105

Check It Out: Example 2 Write 0.00022 in scientific notation. Move the decimal point 4 places to the right. 0.00022 = 0.00022 Write as a product of two factors. = 2.2  0.0001 Write the exponential form. Since the decimal point was moved 4 places, the exponent is 4. = 2.2  104

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 = 0.00078 = 0.00078

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 = 0.0033 = 0.0033

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

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

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