Unit2 #2
Name:_______________________________
Exponents
An exponent tells the number of times a number is used as a ___________________ .
4 is the ___________, and 3 is the _____________________ .
3
4
How to solve? 43 = 4 · 4 · 4 = 64
One way to write a ___________________ is as an expression with a negative __________________ .
Complete the pattern:
22 = 4
21 = 2
20 = _____
Anything to the zero power equals _______ ! (Except for zero)
2−1 = _____
A fraction _______ can be expressed as 2−1 .
Powers of Ten
Positive Powers of 10
Evaluate.
𝟏𝟎𝟑 =
1) 34
2) 4 squared
𝟏𝟎𝟏 =
3) 26
4) x cubed
𝟏𝟎𝟎 =
5) 10−3
6) 10−2
Negative Powers of 10
7) (1.3)2
8) 141
9) 0.7 squared
10) 105
11) (−6)3
12) −(−5)3
13) 50
14) (−6)1
15) −72
16) ( )3
𝟏𝟎𝟐 =
𝟏𝟎−𝟏 =
𝟏𝟎−𝟐 =
𝟏𝟎
−𝟑
=
𝟏𝟎−𝟒 =
If the exponent value
decreases…what happens to the
value of the expression?
________________________
1
2
Scientific Notation
 A number is expressed in _______________________________ when it is written as
the ________________ of a number and a ___________________ of 10.
 The number must be _______________ than or equal to 1 and _______________ 10 .
___________________________________________________________________!
Examples:
Standard Form
5,000,000
Scientific Notation
5.0 × 106
0.000072
7.2 × 10−5
Standard Form → Scientific Notation




Look from left to right. Place the decimal after the first non-zero digit.
Count how many places the decimal point should move from its original position.
The # of moves is recorded as the _______________ in the ________________ .
? Is my number in standard form a small number or a BIG number???? (Less than 1 or greater than 10.)
o If it was a decimal less than 1 (small #), the exponent will be ____________________ .
o If it was a number greater than 10 (BIG #), the exponent will be _________________ .
1) 4,300
2) 57,000,000
3) 0.00026
4) 0.004
5) 12
6) 0.000001
Scientific Notation → Standard Form
Positive exponent: Move the decimal to the right as many spaces as the __________________ . Fill in the
spaces with ___________ . Remember: we want a BIG number!
Examples:
9 × 106
1.0305 × 108
Negative exponent: The result will be ____________________ .
Move the decimal to the left as many spaces as the __________________ . Fill in the spaces with _________ .
Examples:
4.309 × 10−4
7 × 10−3
Write the following numbers in standard form
1) 1.8 × 105
2) 5.04 × 10−5
3) 6.8 × 10−7
4) 2.72 × 109
5) 1.3 × 10
6) 4.08 × 10−1
Comparing and Ordering Numbers in Scientific Notation
DO NOT rewrite them as decimals!
1) To compare two numbers written in scientific notation, first compare the
________________.
The one with the greater exponent will be ____________________.
2) If the exponents are ___________, compare their decimals.
Examples:
1. Compare 6.23 × 𝟏𝟎𝟏𝟒 and 8.912 × 𝟏𝟎𝟏𝟐
2. Which is greater, 5.15 × 𝟏𝟎−𝟒 or 6.35 × 𝟏𝟎−𝟓
3. Compare 3.28 × 𝟏𝟎𝟏𝟕 and 4.25 × 𝟏𝟎𝟏𝟕
4. Order from least to greatest 2.81 × 𝟏𝟎−𝟕 ; 2.01 × 𝟏𝟎𝟑 ; 2.72 × 𝟏𝟎−𝟕 ; 9.45 × 𝟏𝟎−𝟒 .
Compare:
2.56 × 105 _____ 4.2 × 10−7
4.3 × 104 _____ 1.6 × 106
7.1 × 10−2 _____ 2.9 × 10−6
5.27 × 105 _____ 2.139 × 105
In 2005, Hurricane Katrina caused over $125 billion in damage in the southern United States.
Write $125 billion in scientific notation.
HOMEWORK 2.2
1. Evaluate. Show the negative exponent both as a decimal and as a fraction.
1) 104
5) 105
2) 10−1
3) 103
4) 10−3
6) 10−2
7) 100
8) 10−5
2. Write the numbers in scientific notation.
1) 98,000
2) 0.0004
3) 0.0056
4) 0.091
5) 0.0000451
6) 0.0089
7) 158
8) 30,600
9) 0.07345
10) 0.3
11) 0.896
12) 34,967
3. Write the numbers in standard form.
1) 9 × 10−2
2) 4.2 × 104
3) 8.3 × 10−2
4) 1.95 × 10−3
5) 9.02 × 107
6) 2.3 × 10−1
7) 6.032 × 105
8) 8.977 × 10−6
9) 7.25 × 10−4
10) 8.1 × 10−4
11) 4.083 × 109
12) 6.98 × 10−5
4. Compare.
1) 3.5 × 10−4 ____ 2.1 × 10−6;
2) 1.9 × 10−9 ____ 5.3 × 10−9
3) 2.3 × 105 ____ 2.3 × 10−7;
4) 6.279 × 105 ____ 1.8 × 107
5. The table lists the populations of five countries.
List the countries from least to greatest population.
Country
Population
Australia
Brazil
Egypt
Luxemburg
Singapore
2.0 × 107
1.9 × 108
7.7 × 107
4.7 × 105
4.4 × 106
6. Write each fraction as a percent.
1)
𝟑
𝟒𝟎
𝟕
2) 𝟏𝟐𝟓
𝟓
3) 𝟗
𝟏
4) 𝟑