Beginning Algebra, 11th Edition

Using Scientific Notation

Write each number in scientific notation.

(a)93,000,000

Move the decimal point to follow the first nonzero digit (the 9). Count the num-

ber of places the decimal point was moved.

93,000,000. Decimal point

7 places

The number will be written in scientific notation as To find the value of n,

first compare the original number, 93,000,000, with 9.3. Since 93,000,000 is greater

than 9.3, we must multiply by a positivepower of 10 so that the product

will equal the larger number.

Since the decimal point was moved seven places, and since nis positive,

(b)

10 places

(c) 0.00462

Move the decimal point to the right of the first nonzero digit, and count the num-

ber of places the decimal point was moved.

0.00462 3 places

Since 0.00462 is lessthan 4.62, the exponent must be negative.

(d)

5 places

- 0.0000762= -7.62* 10 -^5

0.00462=4.62 * 10 -^3

63,200,000,000=6.3200000000= 6.32* 1010

93,000,000= 9.3* 107.

9.3* 10 n

9.3* 10 n.

EXAMPLE 1

SECTION 5.3 An Application of Exponents: Scientific Notation 313

NOW TRY

NOTE To choose the exponent when you write a positive number in scientific nota-

tion, think as follows.

1. If the original number is “large,” like 93,000,000, use a positiveexponent on 10,

since positive is greater than negative.

2. If the original number is “small,” like 0.00462, use a negativeexponent on 10,

since negative is less than positive.

OBJECTIVE 2 Convert numbers in scientific notation to numbers without

exponents.To do this, we work in reverse. Multiplying a number by a positive

power of 10 will make the number greater. Multiplying by a negative power of 10

will make the number less.

Writing Numbers without Exponents

Write each number without exponents.

(a)

Since the exponent is positive, we make 6.2 greater by moving the decimal point

three places to the right. We attach two zeros.

6.2* 103 =6.2 00 = 6200

6.2* 103

EXAMPLE 2

NOW TRY
EXERCISE 1
Write each number in
scientific notation.

(a)12,600,000

(b)0.00027

(c) -0.0000341

NOW TRY ANSWERS

1. (a)
   (b)
   (c) -3.41* 10 -^5

2.7* 10 -^4

1.26* 107

Remember the

negative sign.