# Objective The student will be able to: express numbers in scientific and decimal notation.

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Objective The student will be able to: express numbers in scientific and decimal notation.

Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

Scientific Notation A number is expressed in scientific notation when it is in the form a x 10 n where a is between 1 and 10 and n is an integer

How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

2.10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 10 23

The Distance From the Sun to the Earth 93,000,000

Step 1 Move decimal left Leave only one number in front of decimal

Step 2 Write number without zeros

Step 3 Count how many places you moved decimal Make that your power of ten

The power of ten is 7 because the decimal moved 7 places.

93,000,000 --- Standard Form 9.3 x 10 7 --- Scientific Notation

Practice Problem 1) 98,500,000 = 9.85 x 10 ? 2) 64,100,000,000 = 6.41 x 10 ? 3) 279,000,000 = 2.79 x 10 ? 4) 4,200,000 = 4.2 x 10 ? Write in scientific notation. Decide the power of ten. 9.85 x 10 7 6.41 x 10 10 2.79 x 10 8 4.2 x 10 6

More Practice Problems 1) 734,000,000 = ______ x 10 8 2) 870,000,000,000 = ______x 10 11 3) 90,000,000,000 = _____ x 10 10 On these, decide where the decimal will be moved. 1)7.34 x 10 8 2) 8.7 x 10 11 3) 9 x 10 10

Complete Practice Problems 1) 50,000 2) 7,200,000 3) 802,000,000,000 Write in scientific notation. 1) 5 x 10 4 2) 7.2 x 10 6 3) 8.02 x 10 11

Scientific Notation to Standard Form Move the decimal to the right 3.4 x 10 5 in scientific notation 340,000 in standard form 3.40000 --- move the decimal

Write in Standard Form 6.27 x 10 6 9.01 x 10 4 6,270,000 90,100

Express 0.0000000902 in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10 -8

Write 28750.9 in scientific notation. 1. 2.87509 x 10 -5 2. 2.87509 x 10 -4 3. 2.87509 x 10 4 4. 2.87509 x 10 5

Express 1.8 x 10 -4 in decimal notation. 0.00018 Express 4.58 x 10 6 in decimal notation. 4,580,000

Write 531.42 x 10 5 in scientific notation. 1..53142 x 10 2 2. 5.3142 x 10 3 3. 53.142 x 10 4 4. 531.42 x 10 5 5. 53.142 x 10 6 6. 5.3142 x 10 7 7..53142 x 10 8

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