Transcript 2-1

2-1 Extension: Negative Exponents
Lesson Presentation
2-1 Extension: Negative Exponents
Learn to evaluate negative exponents and
use them to write scientific notation and
in standard form.
2-1 Extension: Negative Exponents
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.
2-1 Extension: Negative Exponents
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.
2-1 Extension: Negative Exponents
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.
2-1 Extension: Negative Exponents
Additional Example 2: Writing Small Numbers in
Scientific Notation
Write 0.000039 in scientific notation.
0.000039 = 0.000039
Move the decimal point
5 places to the right.
= 3.9  0.00001Write as a product of
two factors.
= 3.9  105
Write the exponential
form. Since the decimal
point was moved 5 places,
the exponent is 5.
2-1 Extension: Negative Exponents
Check It Out: Example 2
Write 0.00022 in scientific notation.
0.00022 = 0.00022
Move the decimal point
4 places to the right.
= 2.2  0.0001 Write as a product of
two factors.
= 2.2  104
Write the exponential
form. Since the decimal
point was moved 4 places,
the exponent is 4.
2-1 Extension: Negative Exponents
Additional Example 3: Writing Small Numbers in
Standard Form
Write 7.8  10–4 in scientific notation.
7.8  10–4 = 0.00078
= 0.00078
Since the exponent is –4,
move the decimal point 4
places to the left.
2-1 Extension: Negative Exponents
Check It Out: Example 3
Write 3.3  10–3 in scientific notation.
3.3  10–3 = 0.0033
= 0.0033
Since the exponent is –3,
move the decimal point 3
places to the left.
2-1 Extension: Negative Exponents
Additional Example 4A: Comparing Numbers Using
Scientific Notation
Compare. Write <, >, or =.
5.2  10–6 ___ 8.1  10–14
10–6 > 10–14
5.2  10–6 > 8.1  10–14
Compare the powers
of ten.
2-1 Extension: Negative Exponents
Additional Example 4B: Comparing Numbers Using
Scientific Notation
Compare. Write <, >, or =.
2.9  10–7 ___ 5.3  10–7
10–7 = 10–7
Compare the powers
of ten.
Since the powers of ten are equal, compare
the decimals.
2.9 < 5.3
2.9  10–7 < 5.3  10–7
2 is less than 5.
2-1 Extension: Negative Exponents
Check It Out: Example 4
Compare. Write <, >, or =.
5.2  10–5 ___ 4.3  10–5
10–5 = 10–5
Compare the powers
of ten.
Since the powers of ten are equal, compare
the decimals.
5.2 > 4.3
5.2  10–5 > 4.3  10–5
5 is greater than 4.