Negative Exponents and Scientific Notation Chapter 4.2

x -a = = xaxa 1 1 xaxa Negative Exponents

a. x Write with positive exponents. x -12

b. w Write with positive exponents. w -5

z -2 z Write with positive exponents. c.

a Evaluate. 4 -3

b Evaluate. 2 -4

w 4 a. 3 w Simplify. Write the expression with no negative exponents.

b. x6x6 z -2 x -6 y4y4 z2z2 3. Simplify. Write the expression with no negative exponents. y4y4

c. x 6 y Simplify. Write the expression with no negative exponents. x -6 y -5

a. ( (2) -2 4 x8x8 y 10 x -8 y Write with positive exponents. 2 x4x4 y -5 ) -2 Use the power rules. Evaluate and write with positive exponents.

b. y 2 y2y2 y -3 y 3 z 4 z 6 y 5 z 2 4. Write with positive exponents. z -4 z -6 Write with positive exponents. Use the quotient rule. Use the product rule.

x -a = = xaxa 1 1 xaxa Negative Exponents

Scientific Notation a a is a number so that 1 ≤ a < 10 n is an integer x 10 n

Two methods to change a number into Scientific Notation 1.Move the decimal point left or right. The number of places is n (left is positive, right is negative) a x 10 n

2.n represents the place value of the first nonzero digit from the original number Here are the place names. These are the exponential form for each place. billions hundred millions ten millions millions hundred thousands ten thousands thousands hundreds tens ones tenths hundredths thousandths ten thousandths hundred thousandths millionths.

x 10 4 a. 78, Write in scientific notation. Count the number of places to move. Positive 4 is the exponent.

x 10 4 a. = 7.82 billions hundred millions ten millions millions hundred thousands ten thousands thousands hundreds tens ones tenths hundredths thousandths ten thousandths hundred thousandths millionths Write in scientific notation. 8,2007 What is the place value of 7?

b. 4,786, x Write in scientific notation. Count the number of places to move. Positive 6 is the exponent.

x 10 6 b. = billions hundred millions ten millions millions hundred thousands ten thousands thousands hundreds tens ones tenths hundredths thousandths ten thousandths hundred thousandths millionths ,786,0604 What is the place value of4?

a x Write in scientific notation. Count the number of places to move. Negative 1 is the exponent.

x a. = 9.8 billions hundred millions ten millions millions hundred thousands ten thousands thousands hundreds tens ones tenths hundredths thousandths ten thousandths hundred thousandths millionths What is the place value of 9?

b x Write in scientific notation. Count the number of places to move. Negative 5 is the exponent.

x b. = 9.2 billions hundred millions ten millions millions hundred thousands ten thousands thousands hundreds tens ones tenths hundredths thousandths ten thousandths hundred thousandths millionths What is the place value of 9?

a x ,930, Write in decimal notation. The exponent is positive 6. Move the decimal point right 6 places. 6

a x = 1,930,000 billions hundred millions ten millions millions hundred thousands ten thousands thousands hundreds tens ones tenths hundredths thousandths ten thousandths hundred thousandths millionths Write in decimal notation What is the place value of 1?

b x Write in decimal notation. The exponent is negative 5. Move the decimal point left 5 places. -5

7. Write in decimal notation. b x = billions hundred millions ten millions millions hundred thousands ten thousands thousands hundreds tens ones tenths hundredths thousandths ten thousandths hundred thousandths millionths What is the place value of 8?

8. Astronomers measure distances to faraway galaxies in parsecs. A parsec is 30,900,000,000,000,000 meters, Write this in scientific notation x m

Using Scientific Notation a x 10 n a is a number so that 1 ≤ a < 10 n is an integer

) Use scientific notation and the laws of exponents to find the following. Leave your answer in scientific notation. a. ( ( 7.84 x ( 56,000 )( 1,400,000,000 ) 5.6 x 10 4 ) x 10 9 Write each in scientific notation. Use the product rule. Multiply the numbers.

b. 9. Use scientific notation and the laws of exponents to find the following. Leave your answer in scientific notation x x x Write each in scientific notation. Write as positive exponents. Divide the numbers. =

b. 9. Use scientific notation and the laws of exponents to find the following. Leave your answer in scientific notation x x x Write in scientific notation. Use the product rule. Use the quotient rule. = x x x 10 2

The average from Earth to the distant star Betelgeuse. would it take a space probe to travel from Earth to Betelgeuse at a ? Round to three significant digits. = (3.09 x ) t = d s (159) (50000) ( ( distance is 159 parsecs (1 parsec = 3.09 x km) speed of 50,000 kilometers per hour How many hours Write in scientific notation. Multiply and use the product rule x 10 2 ) 3.09 x ) 5 x x x 10 4

= 9.83 x ≈ x x Divide and use the quotient rule. Write in scientific notation x x 10 4 Round to three significant digits x Use the product rule

Using Scientific Notation a x 10 n a is a number so that 1 ≤ a < 10 n is an integer

Scientific Notation a x 10 n a is a number so that 1 ≤ a < 10 n is an integer

Negative Exponents and Scientific Notation Chapter 4.2