Brainstorm. Period. Scientific Notation Activity 7 NOTES

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1 Name Scientific Notation Activity 7 NOTES Period By the end of this activity, I will be able to express numbers in scientific notation. By the end of this activity, I will be able to convert numbers in scientific notation to standard form. By the end of this activity, I will be able to use scientific notation to write estimates of quantities. By the end of this activity, I will be able to compare and order numbers in scientific notation. Write the number in decimal form. Write the number in decimal form. Write the following number in standard form. Write the following number in standard form Brainstorm In your groups write down as many quantities you can think of that are represented by very large or very small numbers.

2 The sun has a diameter of m and a mass of kg. The measurements, m and kg, are written in scientific notation. A number written in scientific notation is the product of a factor a, and a power of 10 with an exponent that is an integer n. It is expressed in the form a 10 n, where 1 a < 10 and n is an integer. A number is written in standard form when it is expressed in digits only. Scientific notation is especially helpful when working with numbers that are very large and very small magnitudes. Write the number in decimal form Write the number in decimal form What is the relationship between the exponent of the power of 10 and the number of places the decimal moves?

3 Converting from Scientific Notation to Standard Form Example A Rewrite the diameter of the sun, m in standard form. Step 1 Determine how many places the decimal will move to the right or left. Move the decimal to the right if the exponent is positive or left if the exponents is negative. Step 2 Solution You Try! Rewrite the mass of the sun, kg, in standard form. Rewrite the following expression in standard form: Rewrite the following expression in standard form:

4 Converting from Standard Form to Scientific Form Example B Convert 25,000,000,000 from standard form to scientific notation Step 1 Step 2 Identify the location of the decimal point. Move the decimal point to the left or right until you have a number greater than or equal to 1 and less than 10. Count the number of places you moved the decimal point. Step 3 Rewrite the number in scientific notation. Exponent will be negative if you moved to the right and positive if you moved to the left. Solution You Try! Convert each number from standard form to scientific notation. 6, ,000,

5 Take a guess How many people are there on Earth? Approximately, how much is the U.S. National Debt? How much money does Justin Bieber make in a year? ,000,000,000,000 Comparing Numbers in Scientific Notation Example C The diameter of the Earth is about miles. The diameter of the Sun is about Determine how much bigger the diameter of the Sun is to the diameter of the Earth. Step 1 Step 2 Determine what to multiply the smaller power of 10 by to get the larger power of x =10 5 Estimate how many times the smaller integer will go into the larger integer. Solution

6 You Try! The moon is about miles from Earth. The is about Sun is miles from Earth. How much further is the Sun from Earth? Solution: Ordering Numbers in Scientific Notation Example D Order these numbers from least to greatest: , , Step 1 Use the values of the exponents to help determine the order. Step 2 If possible, write the numbers in standard form to check the order. Solution You Try! Order these numbers from least to greatest , , , ,

7 Name Scientific Notation Activity 7 In-Class Practice Period Convert each number from scientific notation to standard form. 5.2 x x x x 10-6 Convert each number from standard form to scientific notation. 20,000 1,340, Explain how the following numbers need to be changed in order to be correctly written in scientific notation, 15 x x x 10 7

8 Explain why someone would want to write 52,000,000,000,000,000 in scientific notation instead of standard form. Lena converted 1.2 x 10-7 to the standard form 12,000,000. Do you agree with Lena? Explain your reasoning. Order the following numbers from least to greatest..0051, 8 x 10-4, 1.89 x 10-3, The diameter of the moon is about 2.2 x 10-3 miles and the diameter of the Sun is about 8.6 x 10 5 miles. How much larger is the diameter of the sun than the diameter of the moon.

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