Name: ________________________________________
SCIENTIFIC NOTATION & EXPONENTIAL FUNCTIONS STUDY GUIDE
A. KNOW HOW TO CONVERT A NUMBER INTO SCIENTIFIC NOTATION
Step 1: Determine where the decimal point is in the number
Step 2: Determine where would you put the decimal to make this number be between 1 and 10
Step 3: Decide how many decimal places you need to move the decimal
Step 4: Write the new decimal
× 10 𝑛 , 𝑛 =
# of places*
*Note: + if the original number is more than 1, the exponent is positive
- if the original number is less than 1, the exponent is negative
Example: To write 527 in scientific notation, place the decimal point at end of number and move left n decimal places so that the number is between 1 and 10. This would give
5.27x10
n . Since the original number is more than 1 (527>1), the exponent is positive and since we moved 2 decimal places to the left, we get a final answer of
5.27x10
2 .
B. KNOW HOW TO CONVERT A NUMBER INTO STANDARD FORM
Step 1:
Move the decimal point to the right for positive exponents of 10.
Move the decimal point to the left for negative exponents of 10.
The exponent tells you how many places to move.
Step 2: Fill in with zeros
Example: To write
5.43x10
-
3 in standard form, move the decimal left (since exponent is negative) 3 places and fill in with zeros. We get a final answer of .00543.
C. KNOW HOW TO MULTIPLY IN SCIENTIFIC NOTATION i) Multiplying by a number
Step 1: Multiply the number times the coefficient
Step 2: Simplify so that the number is written in correct scientific notation
Example: To multiply 5(
4.13x10
3 ), multiply the 5 x 4.13 to get
20.65 correctly in scientific notation so your answer is
2.065x10
20.65x10
4 .
3 . Now write the ii) Multiplying two numbers in scientific notation
Step 1: Multiply the coefficients
Step 2: Add the exponents
Step 3: Make sure your final answer is written in proper scientific notation
Example: To multiply (
7x10
2 )(
4x10
5 ), multiply the 7 x 4 and add the exponents 2 & 5 to get
28x10
7
.
Now write the 28 correctly in scientific notation so your answer is 2.8x10
8 .

D. KNOW HOW TO DIVIDE NUMBERS IN SCIENTIFIC NOTATION
Step 1: Divide the coefficients
Step 2: Subtract the exponents
Step 3: Make sure your final answer is written in proper scientific notation
95.2x10
-
2
Example: To divide
7x10
7
, first divide 95.2 and 7 to get 13.6. Then subtract the exponents (-
2 – 7) to get -9. This becomes 13.6𝑥10 −9 . And, finally write answer in proper scientific notation to get 1.36x10
-
8
.
E. KNOW HOW TO ORDER NUMBERS IN SCIENTIFIC NOTATION
Step 1: Write every number in correct scientific notation
Step 2: Order each by exponent first and then by coefficient
Example: To order
9.25x10
-
5
,10.8x10
-
3
, and 0.013 from least to greatest, write each number in correct scientific notation. This gives 9.25x10
-
5
,1.08x10
first by exponent then by coefficient. Final answer is
-
2
, and 1.03x10
-
2
9.25x10
-
5
F. KNOW HOW TO EVALUATE AN EXPONENTIAL FUNCTION
Step 1: Plug in the values of the variable and solve.
,1.03x10
-
2
. Now order the numbers
, and 1.08x10
-
2
Example: Evaluate the exponential function, f(x)
=
3 x for x = –2, –1, 0, 1, and 2 . f(
-
2)
=
3
-
2 =
1
3
2
=
1
9 f(0)
=
3
0 =
1 f(2)
=
3
2 =
9 f(
-
1)
=
3
-
1 =
1
=
1 f(1)
=
3
1
=
3
3
1
3
G. KNOW HOW TO GRAPH AN EXPONENTIAL FUNCTION USING A TABLE
Step 1: Plug in the values of the variable and solve.
Step 2: Plot each point and draw curve. Remember the curve will get very close to zero on the left side.
Example:

H. KNOW HOW TO DETERMINE IF A RULE REPRESENTS AN EXPONENTIAL FUNCTION
With a table of values, you first make sure the change in x is constant. Then you look at the ratio of the y's value. If the ratio of the values is the same, then it is an exponential function.
Example: Does the table represent a linear or exponential function?
1
2
120
180
180/120 = 1.5, 270/180 = 1.5, 405/270 = 1.5
Therefore, this is an exponential function.
5 607.5
6 911.25
With a function rule, if the x is not an exponent, then it is a linear function. If the x is an exponent, then it is an exponential function
Example: Does the rule represent a linear or exponential function? a) y = 2 x - 3 This is linear because the exponent on x is one. b) Y = 3 x + 4 is exponential because the variable x is an exponent.

PRACTICE
A. Write each number in scientific notation.
1. 890,000,090 ____________________
2. 605,000 ____________________
3. 706,079 ____________________
4. 1,108.4 ____________________
5. 0 .001234 ____________________
B. Write in standard form.
6. 8.3x10
5 ____________________
7. 9.43x10
4
____________________
8. 7.002x10
-
2
____________________
C. Multiply. Write your answer in correct scientific notation.
9. (4.5x10
-
14
)(5.2x10
3
) ____________________
10. (6.1x10
5
)(1.2x10
-
3
) ____________________
11. 1.3(8.102x10
6
) ____________________
12. 8.5(9.32x10
5
) ____________________
D. Divide. Write your answer in correct scientific notation.
13.
(7.2x10
4
)
(9.4x10
-
11
)
____________________
14.
(3.04x10
5
)
(9.89x10
2
)
____________________
E. Order from least to greatest. Write numbers in correct scientific notation, then order the numbers.
15.
7.235x10
7
,8.6x10
6
, and 8,900,000 _________________________________________
16. 1.03x10
9
, 2.8x10
7
, and 1,035,000,000 ______________________________________

0
1
2
F. Evaluate each exponential function.
17.
f(x)
=
2
·
4 x
for x = –2, –1, 0, 1
18.
f(x)
=
5 x for x = –2, –1, 0, 1
G. Evaluate each exponential function.
19.
Graph 𝑦 = 2 ∙ 4 𝑥
using the table below.
x 2 ∙ 4 𝑥 (x, y)
-2
-1
H. Does the rule or table represent a linear or exponential function? Explain.
20.
𝑦 = 2𝑥
21. x 0 1 2 3 f(x) -6 -1 4 9