Buksis-2.4 Revisi Akhir

2.4 What are you going to learn? À To express a number in the scientific notation À To change a scientific notation into a general form

The Meaning of Scientific Notations According to Astronomy, the weight of the earth is about 5,880,000,000,000,000,000,000,000 kg and the

volume

of

the

sun

is

about

1,330,000,000,000,000 km 3 . How do you read the numbers? You might have some difficulties, since

Key Terms

those numbers are very large, and they have so

• • •

many

Scientific notation Digit General form

zero

digits.

You

might

also

have

difficulties in reading the mass of a water molecule.

It

is

estimated

that

the

mass

is

0.00000000000000000003 gram. To reduce the possibility of making mistakes in reading or writing such numbers, we may use the method called scientific notation.

Scientific notation is a short way to write a very large or a very small number.

It is written as

multiplication of two factors. The first factor is a number greater than or equal to 1 but less than 10, and the second factor is ten to the n th power. a x 10n where n is an integer and 1 ≤ a < 10

Mathematics for Junior High School – Year 7/ 103

The Scientific Notation Before

discussing

the

method

to

convert

a

number into a scientific notation, examine the following number of ten to the n th power.

10 4 = 10.000

There are 4 zeros on the right side of 1.

10 3 = 1000

There are 3 zeros on the right side of 1.

10 2 = 100

There are 2 zeros on the right side of 1 There is 1 ze ro on the right side of 1.

10 1 = 10 10 0 = 1 10 −1 =

1 = 0 .1 101

10 − 2 =

1 = 0.01 10 2

10 − 3 =

1 = 0.001 103

There are 3 zeros on the left side of 1.

10 − 4 =

1 = 0.0001 10 4

There are 4 zeros on the left side of 1.

There is 1 ze ro on the left side of 1.

There are 2 zeros on the left side of 1

Relation with the Real World

Astronomy . The weight of the earth is about 5,880,000,000,000,000,000,000,000 kg. Write down this number in the scientific notation.

5,880,000,000,000,000,000,000,000 24 digits = 5.88 x 1,000,000,000,000,000,000,000,000 = 5.88 x 10 24

104 / Student’s Book – Fractions

The power of 10 is 24.

Write down 0.000056 in scientific notation. 0.000056 5 places

= 5.6 x 0,00001

Move th e comma 5 places to the right to obtain the factor that is greate r than 1 but less than 10.

= 5.6 x 10 -5

The power of 10 is – 5

Relation with the Real World Domestic spiders usually have a weight of 10 -4 kg. Express the weight of the spider as a fraction and a decimal. 1 104 1 = 10000 = 0.0001

10 − 4 = The wolf spider is usually dark brown. This spider hunts its preys at night. It runs much faster than its preys do. The wolf spider cannnot build its own web.

Definition of negative power Simplify. Expressed as a decimal.

You can convert a number from its scientific notation into its general form.

Write down (a) 1.9 x 10 5 and (b) 4.519 x 10 -4 into general form.

a. 1.9 x 10 5 = 190000 5 places

A positive power shows a great number. Move the comma 5 places to the right.

= 190,000

b. 4.519 x 10 -4 = 0004.519

A negative power shows a small number. Move the comma 4 places to the left.

4 places

= 0.0004519

Mathematics for Junior High School – Year 7/ 105

1.

Write the following numbers in scientific

notations. a. 45,600

b. 0.000000013

c. 80,000,000

d. 0.0002

e. 23,000

f. 0.0101

g. 0.000981

h. 250,000

2. Choose A, B, C, or D. Which of the following is scientific notation of 0.000072? A. 72 × 10 -6

B. 7.2 x 10 5

C. 7.2 x 0,00001

D. 7.2 x 10 -5

3. Write the following numbers into general forms. a. 7 x 10 -9

b. 1.362 x 10 8

c. 4.02 x 10 -5

d. 7.89 x 10 6

e. 9.5 x 10 -1

f. 5

g. 7 x 10 7

h. 3.6 x 10 -3

10 -4

4. Choose A, B, C, or D. Which of the following numbers is equal to 6 x 10 -4 ? A. -60,000 B. 0.00006

The average distance to the sun Earth Jupiter Mars Mercury Neptune

C.

6 10, 000

D. -0.0006

5. The inner temperature of the sun is greater than 16,000,000 0C. Write down scientific notation of the temperature.

Saturn Uranus Venus

6. Astronomy . Put in order the planets in the figure on the left, based on their distances from

106 / Student’s Book – Fractions

the sun. Start from the one closest to the sun.

7.

Biology.

One

litre

equals

to

10 6

cubic

millimetres (mm 3 ). There are 5 x 10 6 red-blood cells in 1 mm 3 of blood. Use scientific notation to express the number of the red-blood cells in 1 litre of human blood.

Mathematics for Junior High School – Year 7/ 107

108 / Student’s Book – Fractions