Intermediate Algebra (11th edition)

272 CHAPTER 5 Exponents, Polynomials, and Polynomial Functions

Writing Numbers in Scientific Notation

Write each number in scientific notation.

(a)820,000

Step 1 Place a caret to the right of the 8 (the first nonzero digit) to mark the new

location of the decimal point.

(^8) ^20,000

EXAMPLE 9

Step 2 Count from the decimal point, which is understood to be after the last 0,

to the caret.

. Decimal point

Count 5 places.

Step 3 Since 8.2 is to be made greater, the exponent on 10 is positive.

(b)0.0000072

Count from left to right.

6 places

Since the number 7.2 is to be made less, the exponent on 10 is negative.

(c) Remember the negative sign.

Count 4 places. NOW TRY

- 0.000462= -4.62 * 10 -^4

0.0000072= 7.2* 10 -^6

0.000007. 2

820,000=8.2* 105

8 .20,000

Converting from Scientific Notation to Standard Notation

Write each number in standard notation.

(a)

Attach 0’s as necessary.

7 places

We moved the decimal point 7 places to the right. (We had to attach five 0’s.)

(b)

Attach 0’s as necessary.

3 places

We moved the decimal point 3 places to the left.

or

(c) -1.083 100 =-1.083 1 =-1.083 NOW TRY

4.7* 10 -^3 = .0047, 0.0047

00 4.7

4.7* 10 -^3

6.93 * 107 =69,300,000

6.93 00000

6.93* 107

EXAMPLE 10

Add a leading 0,

since the decimal is

between 0 and 1.

NOW TRY
EXERCISE 9
Write each number in
scientific notation.

(a)7,560,000,000

(b) -0.000000245

NOW TRY
EXERCISE 10
Write each number in
standard notation.

(a)

(b) -5.9* 10 -^5

4.45* 1010

NOW TRY ANSWERS

9. (a)
   (b)


10. (a)44,500,000,000
    (b)-0.000059

• 2.45* 10 -^7

7.56* 109

Converting a Positive Number from Scientific Notation

Multiplying a positive number by a positive power of 10 makes the number

greater, so move the decimal point to the right if nis positive in

Multiplying a positive number by a negative power of 10 makes a number less, so

move the decimal point to the left if nis negative.

If nis 0, leave the decimal point where it is.

10 n.