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**Warm-Up: Put the following items in order from smallest to largest:**

Shoe Solar System Water Molecule Universe Earth Ant Atlantic Ocean Colorado Milky Way Peanut Sand grain Jupiter’s orbit Atom

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**Answer: Atom (nm) Water molecule Sand grain Ant (mm) Peanut Shoe**

Colorado (km) Atlantic Ocean Earth Jupiter’s Orbit Solar System (a.u.) Milky Way Universe (light years

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**Scientific Notation in Astronomy**

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Powers of Ten Website

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**What is Scientific Notation?**

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

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**Why do we use scientific notation?**

Scientific Notation was developed in order to easily represent numbers that are either very large or very small. Here are two examples of large and small numbers. They are expressed in decimal form instead of scientific notation to help illustrate the problem. The Andromeda Galaxy (the closest major galaxy to our Milky Way galaxy) contains at least 200,000,000,000 stars. On the other hand, the weight of an alpha particle, which is emitted in the radioactive decay of Plutonium-239, is ,000,000,000,000,000,000,000,006,645 kilograms. As you can see, it could get tedious writing out those numbers repeatedly. So, a system was developed to help represent these numbers in a way that was easy to read and understand: Scientific Notation.

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**The Distance From the Sun to the Earth**

The distance of the Earth to the sun is 93,000,000 (93million miles).

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**Distance to the Sun in Scientific Notation: Step 1**

Move decimal left Leave only one number in front of decimal Example: 93,000,000 =

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Step 2 Write number without zeros Example: 93,000,000 = 9.3

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**Step 3 7 93,000,000 = 9.3 x 10 Count how many places you moved decimal**

Make that your power of ten Example: 93,000,000 = 9.3 x 10 7

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**Practice Problem Standard to Scientific Notation**

Write in scientific notation. Decide the power of ten. 98,500,000 = 9.85 x 10? 64,100,000,000 = 6.41 x 10? 279,000,000 = 2.79 x 10? 4,200,000 = 4.2 x 10? 9.85 x 107 -----> 6.41 x 1010 -----> 2.79 x 108 -----> -----> 4.2 x 106

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**More Practice Problems**

On these, decide where the decimal will be moved. 734,000,000 = ______ x 108 870,000,000,000 = ______x 1011 90,000,000,000 = _____ x 1010 Answers 3) 9 x 1010 7.34 x 108 2) 8.7 x 1011

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**Complete Practice Problems (Start to Finish)**

Write in scientific notation. 50,000 7,200,000 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

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**Scientific Notation to Standard Form**

Move the decimal to the right 3.4 x 105 in scientific notation move the decimal ---> 340,000 in standard form

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**Move the decimal to the right.**

Write in Standard Form Move the decimal to the right. 6.27 x 106 9.01 x 104 6,270,000 90,100

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