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Evaluate and multiply by powers of 10. Convert between standard notation and scientific notation. Section 6.5Objectives

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Powers of 10 can be used to read and write very large and very small number, such as the masses of atomic particles.

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In algebra, you use more often than to represent multiplication. For example,. Scientific Notation is the exception. You write not.

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The table shows relationships between several powers of 10. ________________________________ _________________________ What do you notice about the decimal point when you divide by 10? The exponent decreases by 1 and the decimal point moves one place to the left.

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The table shows relationships between several powers of 10. The exponent increases by 1 and the decimal point moves one place to the right. ___________________________ _________________________________ What do you notice about the decimal point when you multiply by 10?

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Find the value of each power of 10. Start with 1 and move the decimal point six places to the left. A. 10 –6 C B ,000,000,000 Start with 1 and move the decimal point four places to the right. Start with 1 and move the decimal point nine places to the right. 10, Example 1: Evaluating Powers of 10

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Write each number as a power of 10. A. 1,000,000 The decimal point is six places to the right of 1, so the exponent is 6. B C. 1,000 The decimal point is four places to the left of 1, so the exponent is –4. Example 2: Writing Powers of 10 The decimal point is three places to the right of 1, so the exponent is 3.

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If you do not see a decimal point in a number, it is understood to be at the end of the number. Reading Math

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You can also move the decimal point to find the value of any number multiplied by a power of 10. You start with the number rather than starting with 1. Multiplying by Powers of 10

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Find the value of each expression. A ,389,000,000 Move the decimal point 8 places to the right. B. 467 10 – Move the decimal point 3 places to the left. C Move the decimal point 2 places to the left Example 3: Multiplying by Powers of 10

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Scientific notation is a method of writing numbers that are very large or very small. A number written in scientific notation has two parts that are multiplied. The first part The second part is a power of 10.

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The first part is a number needs to be greater than or equal to 1 and less than 10. The second part is a power of 10.

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Convert the following to scientific notation, if necessary. A. 15 10 3 Move the decimal point 1 place to the left. Add 1 to the exponent. 1 5 B. 985 10 6 Example 4: Converting to Scientific Notation 1.5 10 4 Move the decimal point 2 places to the left. Add 2 to the exponent 10 8 C Move the decimal point 3 places to the right. Minus 3 to the exponent.

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Example 5: Astronomy Application Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km. Write Saturn’s diameter in standard form ,000 km Move the decimal point 5 places to the right.

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Write Saturn’s distance from the Sun in scientific notation. 1,427,000,000 9 places Example 6: Astronomy Application Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km. Count the number of places you need to move the decimal point to get a number between 1 and 10. Use that number as the exponent of 10 9 km

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