CONFIDENTIAL 1

Grade 8 Grade 8

Exponents/Scientific Exponents/Scientific NotationNotation

Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific Notation is based on

powers of the base number 10.

The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always

written in exponent form. In the number 1.23 x 1011 the number 11 is referred to

as the exponent or power of ten.

Scientific notation

The number 123,000,000,000 in scientific notation is written as : 1.23 ×1011

The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10.

Exponents

The "exponent" stands for however many times the thing is being multiplied. The thing that's being

multiplied is called the "base". This process of using exponents is called "raising to a power", where the

exponent is the "power". "53" is "five, raised to the third power".

Example 1: 2 x 2 x 2 x 2 x 2 = 25

i.e., 2 raised to the fifth power

Exponential notation is an easier way to write a number as a product of many factors.

Whole numbers can be expressed in standard form, in factor form and in exponential form. Exponential notation makes it easier to write a number as a factor repeatedly. A number written in exponential form is a base raised to an exponent. The exponent tells us how many times the

base is used as a factor.

Write 103, 36, and 18 in factor form and in standard form.

ExponentialForm

FactorForm

StandardForm

103 10 × 10 × 10 1,000

36 3 ×3 ×3 × 3 × 3 ×3 729

18 1 ×1 × 1 ×1 × 1 × 1 × 1 × 1 1

If a negative number is raised to an even power, the result will be positive.

(-2)4 = - 2 × - 2 × - 2 × - 2 = 16

If a negative number is raised to an odd power, the result will be negative.

(-2)5 = - 2 × - 2 × - 2 × - 2 × - 2 = -32

The negative number must be enclosed by parentheses to have the exponent apply to the negative term.

Note that (-2)4 = - 2 × - 2 × - 2 × - 2 = 16 and -24 = -(2 × 2 × 2 × 2) = -16

Write in scientific notation: 35,800

Place the decimal point between the first two non-zero numbers, 3 and 5.

Since the 3 was in the ten-thousands place, the power of 10 is 104.

The number in the scientific notation is 3.58 × 104.

To change the number from scientific notation into standard notation, you can also count the number of times

the decimal point moved to determine the power of 10.

35,800 = 3 5 8 0 0 = 3.58 × 104

Decimal point moves 4 places to the left.

To change the number from scientific notation into standard notation, begin with place value

indicated by the power of 10. Add zeroes as place holders when necessary.

0.0079 = 0. 0 0 7 9 = 7.9 × 10-3

Write in scientific notation: 0.0079

Decimal point moves 3 places to the right.

Let us do some practice problems!

CONFIDENTIAL

9

1) What is the number 0.000512 denoted as in the scientific notation?

a) 51.2 × 104

b) 51.2 × 10-4

c) 5.12 × 104

d) 5.12 × 10-4

d) 5.12 × 10-4

CONFIDENTIAL 10

2) What is the number 1.512 × 106 denoted as in the standard notation?

a) 1512000000b) 1512000c) 151200000d) 15120000

b) 1512000

CONFIDENTIAL 11

3) Pluto’s mean distance from Sun is 3,670,000.000 miles. What is this number in the scientific notation?

a) 3.67 × 109 milesb) 3.67 × 108 milesc) 3.67 × 107 milesd) 3.67 × 1011 miles

a) 3.67 × 109 miles

CONFIDENTIAL 12

4) To write 3.18 ×107 in standard notation, how many times will the decimal point move?

a) 7 places to the right.b) 5 places to the right.c) 7 places to the left.d) 5 places to the right.

a) 7 places to the right.

CONFIDENTIAL 13

5) Which number is the largest?

a) 3.67 × 10-9

b) 3.67 × 10-8

c) 3.67 × 10-7

d) 3.67 × 10-11

c) 3.67 × 10-7

CONFIDENTIAL 14

6) A movie grossed nearly 6.7 × 106 dollars. What is this number in standard form.

a) $0.000067b) $6,700,000c) $670,000d) $67,000,000

b) $6,700,000

CONFIDENTIAL 15

7) A micrometer is 0.000001 meter. Which expression represents this number in scientific notation?

a) 1.0 × 107 meterb) 1.0 × 106 meterc) 1.0 × 10-5 meterd) 1.0 × 10-6 meter

d) 1.0 × 10-6 meter

CONFIDENTIAL 16

8) What is 237 raised to the first power in the scientific notation?

a) 2.37 × 103

b) 2.37 × 102

c) 2.37 × 10-2

d) 2.37 × 10-3

b) 2.37 × 102

CONFIDENTIAL 17

a) 8 × (1.03)8

b) 8 × (1.03)7

c) 8 × (1.03)6

d) 8 × (1.03)9

9) The cost of a movie ticket is $8, which increases by 3% each year. Find the cost of the ticket after 8 years.

Year Cost

1 8 × (1.03)

2 8 × (1.03)2

3 8 × (1.03)3

4 8 × (1.03)4

a) 8 × (1.03)8

CONFIDENTIAL 18

10) A teacher asked four students for the value of 4 × 103, Chris said 400, Ed said 4,000, Jake said 40,000 and Gary said 400,000. Who among the

four is correct?

a) Chrisb) Edc) Jaked) Garyb) Ed

Assessment

CONFIDENTIAL

20

1) What is the number 961400000 denoted as in the scientific notation?

a) 9.614× 108

b) 9.614 × 10-8

c) 9.614 × 107

d) 9.614 × 10-7

a) 9.614× 108

CONFIDENTIAL 21

2) What is the number 7.03 × 10-5 denoted as in the standard notation?

a) 0.00000703b) 0.000703c) 0.00703d) 0.0000703

d) 0.0000703

CONFIDENTIAL 22

3) Jake wrote a guess of 7,800 for the number of of jar. What is this number in the scientific notation?

a) 7.8 × 10-4

b) 7.8 × 103

c) 7.8 × 10-2

d) 7.8 × 101

b) 7.8 × 103

CONFIDENTIAL 23

4) A certain bacterium is approximately 1.8 × 10-7 mm long. How is length expressed in standard notation?

c) 0.00000018 mm.

a) 0.000018 mmb) 0.0000018 mmc) 0.00000018 mmd) 0.0018 mm

CONFIDENTIAL 24

5) Which number is the larger than 5.8 × 10-3?

a) 6 × 10-4

b) 5.8 × 10-4

c) 5 × 10-3

d) 5.9 × 10-3

d) 5.9 × 10-3

CONFIDENTIAL 25

6) Light takes about 5.4 × 10-6 second to travel one mile. What is this number in standard form.

a) 0.0000054b) 0.000054c) 0.0000054d) 0.00000054

a) 0.0000054

CONFIDENTIAL 26

7) To write 3.18 × 10-3 in standard notation, how many places will the decimal point move?

b) 3 places to the left.

a) 3 places to the right.b) 3 places to the left.c) 4 places to the left.d) 4 places to the right.

CONFIDENTIAL 27

8) What is 2×103 + 4×102 + 7×101 in the standard form?

a) 2470 b) 24700c) 2407d) 247

a) 2470

CONFIDENTIAL 28

9) Rents in a particular area are increasing by 10% every year. Predict what would be the rent of the

apartment after 2 years, if its rent is $100 per month now?

a) $105b) $110c) $120d) $121

d) $121

CONFIDENTIAL 29

10) There are 20 elephants in a zoo. What will be their population after 2 years, if the population

doubles each year?

a) 40 elephantsb) 80 elephantsc) 60 elephantsd) 20 elephants

b) 80 elephants

You did a great job today!