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6-1 Scientific Notations

Geogebra Writing in Standard Form

Write large numbers in scientific notation In this lesson you will learn how to write very large numbers by using scientific notation. Standards: 8.EE.A.3 Write small numbers in scientific notation In this lesson you will learn how to write a very small number by using scientific notation. Standards: 8.EE.A.3 Compare large numbers using scientific notation In this lesson you will learn how to make rough comparisons of very large numbers by using scientific notation. Standards: 8.EE.A.3 Compare small numbers using scientific notation In this lesson you will learn how to make rough comparisons of very small numbers by using scientific notation. Standards: 8.EE.A Videos

Video Tutor Help Scientific notation: order from greatest to least Writing a number in standard notationWriting a number in standard notation (6-1) Scientific Notation Scientific Notation with Negative Exponents Khan Academy 6-1 Scientific Notation Course 3 Scientific Notation Scientific notation allows us to more easily express very large or very small numbers encountered in engineering and science. Using exponents, we can convert standard decimal numbers into scientific notation and vice versa.

Worksheets 6-1 Note-Taking Guide 6-1 Practice 6-1 Guided Problem Solving

Vocabulary Practice Chapter 6 Vocabulary (Electronic) Flash Cards

Additional Lesson Examples 6-1 Step-by-Step Examples

Lesson Readiness 6-1 Problem of the Day 6-1 Lesson Quiz

Powers of 10 are used when writing numbers in scientific notation. Scientific notation is a way to express numbers that are very large or very small. Numbers written in scientific notation are expressed as 2 factors. One factor is a number greater than or equal to 1. The other factor is a power of 10.

Why does a Negative Exponent give us a small number? = 10 x 10 x 10 x 10 = = 10 x 10 x 10 = = 10 x 10 = = = 10 0 Do you see a pattern?

Sooooo = = = = = = = 10 -4

The table shows relationships between several powers of 10. Each time you divide by 10, the exponent decreases by 1 and the decimal point moves one place to the left.

The table shows relationships between several powers of 10. Each time you multiply by 10, the exponent increases by 1 and the decimal point moves one place to the right.

You may need to add zeros to the right or left of a number in order to move the decimal point in that direction. Writing Math

The table shows relationships between several powers of 10. Each time you divide by 10, the exponent in the power decreases by 1 and the decimal point in the value moves one place to the left. Each time you multiply by 10, the exponent in the power increases by 1 and the decimal point in the value moves one place to the right.

You can find the product of a number and a power of 10 by moving the decimal point of the number. You may need to write zeros to the right or left of the number in order to move the decimal point.

A. 14  10 4 Multiply Since the exponent is a positive 4, move the decimal point 4 places to the right. Additional Example 1: Multiplying by Powers of Ten 140,000 B. 3.6  10  Since the exponent is a negative 5, move the decimal point 5 places to the left

Additional Example 2: Writing Numbers in Scientific Notation Think: The number is less than 1, so the exponent will be negative. A Think: The decimal needs to move 3 places to get a number between 1 and  10 3 Write the number in scientific notation. So written in scientific notation is 7.09  10 –3.

Additional Example 2: Writing Numbers in Scientific Notation Think: The number is greater than 1, so the exponent will be positive. B. 23,000,000,000 Think: The decimal needs to move 10 places to get a number between 1 and  Write the number in scientific notation. So 23,000,000,000 written in scientific notation is 2.3 

,000 Think: Move the decimal right 5 places. A   10 5 Additional Example 3: Reading Numbers in Scientific Notation Write the number in standard form.

Think: Move the decimal left 3 places. 2.7  10 –3 B. 2.7  10 –3 Write the number in standard form. Additional Example 3: Reading Numbers in Scientific Notation

Example 9-1a Notice that the decimal place moves 5 places to the right. Answer: 962,000 Write in standard form. or 100, ,000 Express Numbers in Standard Form Writing in Standard Form

Example 9-2a Answer: Write in standard form. Notice that the decimal point moves 6 places to the left. Express Numbers in Standard Form

Express in standard form. Example 8-1a Answer: 43,950 Move the decimal point 4 places to the right. Express Numbers in Standard Form

Example 8-1b Answer: Move the decimal point 6 places to the left. Express in standard form. Express Numbers in Standard Form

At one point, the distance from Earth to the moon is  in. Write this number in standard form. Scientific Notation LESSON 6-1 = 15,134,310,000 At one point, the distance from Earth to the moon is 15,134,310,000 in  = Move the decimal 10 places to the right. Insert zeros as necessary.. Additional Examples

Example 9-3a Write 931,500,000 in scientific notation. Answer: The decimal point moves 8 places. The exponent is positive. Write Numbers in Scientific Notation

Example 8-2c Express in scientific notation. The exponent is negative. The decimal point moves 2 places. Answer: Express Numbers in Scientific Notation

Example 8-2b Express 1,320,000 in scientific notation. The exponent is positive. The decimal point moves 6 places. Answer: Express Numbers in Scientific Notation

Example 8-2c Express in scientific notation. The exponent is negative. The decimal point moves 2 places. Answer: Express Numbers in Scientific Notation

The diameter of the planet Jupiter is about 142,800 km. Write this number in scientific notation. Scientific Notation LESSON ,800 = 1 42,800. The diameter of the planet Jupiter is about  10 5 km. The decimal point moves 5 places to the left.. =  10 5 Use 5 as the exponent of 10. Additional Examples

Example 9-4a Write in scientific notation. Answer: The decimal point moves 3 places. The exponent is negative. Write Numbers in Scientific Notation

Write 4.86 x 10 –3 in standard form. Scientific Notation LESSON 6-1 = x 10 –3 = Move the decimal point 3 places to the left to make 4.86 less than 1. Additional Examples

Write using scientific notation. Scientific Notation LESSON = Move the decimal point 6 places to the right to get a factor greater than 1 but less than 10. = 5.9 x 10 –6 Use 6 as the exponent of 10. Additional Examples

A certain cell has a diameter of approximately 4.11  meters. A second cell has a diameter of 1.5  meters. Which cell has a greater diameter? 4.11   Compare the exponents. Additional Example 4: Comparing Numbers in Scientific Notation Compare the values between 1 and 10. The first cell has a greater diameter > 1.5 Notice that 4.11  > 1.5 

Lesson Review! Write each number in standard form   10 – ,000,000 17,  10 –3 5.7  10 7 Write each number in scientific notation. 5. Order the numbers from least to greatest. T 2  10 –4, 9  10 –5, 7  10 –5 7  10 –5, 9  10 –5, 2  10 –4 6. A human body contains about 5.6  10 6 microliters of blood. Write this number in standard notation. 5,600,000