Scientific Notation

How Many Stars Can You See? Warm-Up How many stars can be seen with the unaided eyes in an urban area? How many stars can be seen with unaided eyes in a rural area? How many stars can be seen with binoculars? How many stars can be seen with a small telescope? How Many Stars Can You See? Unaided Eye in Urban Area 3 x 10 stars Unaided Eye in Rural Area 2 x 10 stars With Binoculars With Small Telescope 2 3 4 6

In your Math Journal on S write… Scientific notation is a compact way of writing very large or very small numbers. X 10 Factor greater than or equal to 1, but less than 10. Power of 10 written in exponential form Notacion cientifica – manera de expresar numeros como el producto de un numero que es al menos igual a 1, pero menor que 10, por una potencia de 10.

4 Write 5.34 x 10 4 5.34 x 10 = 53400 = 53,400 The decimal point moves 4 places to the right.

- 3 Write 3.27 x 10 - 3 3.27 x 10 = 0.00327 The decimal point moves 3 places to the left.

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Example Problems Write each number in standard form 7.42 x 10 Escribe cada número en forma estándar 7.42 x 10 5

Write each number in standard form Escribe cada número en forma estándar - 2 6.8 x 10

Write each number in standard form Escribe cada número en forma estándar 2 3.714 x 10

Standard Form to Scientific Notation To write a number in scientific notation, follow these steps: Move the decimal point to the right of the first nonzero digit Count the number of places you moved the decimal point. Find the power of 10. If the original number was between 0 and 1, the exponent is negative. Otherwise, the exponent is positive.

Write 3,725,000 in scientific notation. 3,725,000 = 3.725 x 1,000,000 = 3.725 x 10 The decimal point moves 6 places. 6 Since 3,725,000 is > 1, the exponent is positive.

Write 0.000316 in scientific notation. 0.000316 = 3.16 x 0.0001 The decimal point moves 4 places. - 4 Since 0 < 0.000316 > 1, the exponent is negative.

Example Problems Write each number in scientific notation 14,850,000 Escribir cada número en notación científica 14,850,000

Write each number in scientific notation Escribir cada número en notación científica 0.00976

Write each number in scientific notation Escribir cada número en notación científica 0.174

Applications of Scientific Notation Up Next… Activity 1: Applications of Scientific Notation