count the number of digits to the right of the first digit (ex: there are six digits to the right of the two in 2,500,000). • Move the decimal place to the left so that it is to the right of the first digit and add the notation x10# of digits (ex: 2,500,000 = 2.5×106). 2 Rules for very small numbers: • For very small numbers, count the number of digits that come after the decimal point up to the first significant digit (ex: there are six digits to the right of the decimal point in 0.0000051). • Move the decimal point so that it is to the right of the first digit and add the notation x10-# of digits (ex: 0.0000051 = 5.1×10-6). Basically, you are counting the number of times the decimal point “jumps”. If it jumps to the left (for big numbers) your notation is positive (x106) and if it jumps to the right (for small numbers) the notation is negative (x10-6). NOTE: ONLY USE SCIENTIFIC NOTATION WHERE PRACTICAL!!! Answer the following: Write the following values in scientific notation with only one value to the left of the decimal (similar to the examples in the video on Canvas): (2 pts) 173,040 _______ 0.000000266 _______ 0.00008 _______ 4,543,000,000 _______ Exercise 1. Calculating rates and unit conversion Complete the following calculations. ALWAYS: • Make sure you calculate the correct answer by writing out your unit conversion per instructions in the “Unit Conversion” section of this lab and in the video provided on Canvas. • Report answer in proper number of significant figures as outlined in the “Significant Figures” section of this lab and in the video provided on Canvas. • Report answers in metric system (mm, cm, m and km) unless specified otherwise. (a) The moon formed approximately 4.55 billion years ago after an impact between a Mars-sized body and proto-Earth. Shortly after its formation, the Moon orbited Earth at a distance of only 25,000 miles. In kilometers, what was the distance between the Earth and Moon at this time? Remember sig figs. (3 pts) (b) Currently the Moon orbits the Earth at a distance of 385,000 kilometers. At what rate has the Moon moved away from the Earth over the past 4,550,000,000 years assuming the Moon started at the position you calculated in question (a)? Report your answer in km/yr. (4 pts) 3 (c) In terms of actual change in distance per year, does your answer for (b) is not a very practical unit. In other words, it is not easy to perceive what the distance the Moon moves in a year looks like and is difficult to work with numbers that small. For this reason, we tend to convert them to a unit that is more practical – one that we can actually estimate the size of in our heads. Convert your answer to (b) to cm per year. (3 pts) (d) Ok, let’s now think about the growth rate of the Himalayan Mountains. The Himalayas started forming 50,000,000 years (or 50 mega-annum, Ma) ago when India crashed into Eurasia. Since that time, they have grown from approximately 0 km in height to 8.8 km in height. Calculate the growth rate of the Himalayan Mountains in km/Ma (kilometers per mega-annum). (4 pts) (e) The units km/Ma is difficult to comprehend since we don’t know what a million years feels like. Use the space below to convert your answer to mm/yr. (3 pts) (f) Now let’s think about something that moves fast. Earthquake waves are energy waves that move through rock and along the surface of the Earth. The fastest type of earthquake waves travel approximately 4800 meters per second in granite (a rock type we will talk about later in the semester). What is the velocity of these earthquake waves through granite in miles per minute? Remember to report your answer in the correct number of significant figures.
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