Writing Numbers That Are Too Big or Too Small in Decimal Form SCIENTIFIC NOTATION Writing Numbers That Are Too Big or Too Small in Decimal Form

Definitions Scientific Notation Power of Ten Negative Exponent A number between one and ten, including one, multiplied by a power of ten. Power of Ten A product of multiplying ten by itself one or more times. Negative Exponent The opposite of a power of a number; used to express smaller numbers.

Standard Notation to Scientific Notation 137,000,000 can be rewritten as Scientific Notation: 1.37× 10 8

Steps Write 312,000,000,000 in Scientific Notation. Step One Move the decimal place to the left to create a new number from 1 up to 9. Where is the decimal point in 312,000,000,000? Because this is a whole number, the decimal point is understood to be at the end of the number: 312,000,000,000 Decimal Point

Steps 312,000,000,000 becomes Step Two Step Three 3 12 Drop all zeros 3 12 Step Two Drop all zeros Step Three Count the number of places from the old decimal point to the new decimal point. In this case, there are 11 places.

Steps 312,000,000,000 3 12 Step Four Multiply by power of 10 and add the exponent: 3 12 x 10 11

Practice Rewrite the Standard Notation numbers as Scientific Notation: 347,000 3.47× 10 5 902,000,000 9.02× 10 8 61,400 6.14× 10 4

Scientific Notation to Standard Notation The process is reversed in two steps! 1.23× 10 5 Step One Look at the exponent: 10 5 Step Two Move the decimal point five places to the right! 123,000

Practice Rewrite the Scientific Notation numbers as Standard Notation: 6.806× 10 6 4× 10 3 2× 10 6 3.104× 10 11 6,806,000 4,000 2,000,000 310,400,000,000

Mixed Review 32,300 2.612× 10 6 16.12 3.06× 10 4 6.1028× 10 10 3.23× 10 4 2,612,000 1.612× 10 1 30,600 61,028,000,000

Practice In the United States, 15,000,000 households use private wells for their water supply. Write this number in scientific notation. 1.5× 10 7

Practice The U.S. has a total of 𝟏.𝟐𝟗𝟏𝟔× 𝟏𝟎 𝟕 acres of land reserved for state parks. Write this in standard form. 12,916,000 acres

Negative Exponents 1000 = 10 x 10 x 10 = 103 100 = 10 x 10 = 102 10 = 101 1 = 100 Do you see a pattern? Can you guess what the next exponent will be?

Negative Exponents 1 = = = = 10-4

Practice Rewrite the following decimals with negative exponents. 0.00082 8.2 X 10-4 0.00000059 5.9 X 10-7 0.00004 4 X 10-5

Practice 1.248× 10 −6 .000001248 6.123 × 10 −5 .00006123 0.00000306 𝟑.𝟎𝟔× 𝟏𝟎 −𝟔 0.000892 𝟖.𝟗𝟐 × 𝟏𝟎 −𝟒

Practice The nucleus of a human cell is about 7× 10 −6 meters in diameter. Write this number in standard notation. .000007

Practice A ribosome, another part of a cell, is about 0.000000003 of a meter in diameter. Write the length in scientific notation. 𝟑× 𝟏𝟎 −𝟗