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

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

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

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. _________________________________________________________

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

Example 1: Evaluating Powers of 10 Find the value of each power of 10. A. 10–6 B. 104 C. 109 Start with 1 and move the decimal point six places to the left. 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. 0.000001 10,000 1,000,000,000

Example 2: Writing Powers of 10 Write each number as a power of 10. A. 1,000,000 B. 0.0001 C. 1,000 The decimal point is six places to the right of 1, so the exponent is 6. The decimal point is four places to the left of 1, so the exponent is –4. The decimal point is three places to the right of 1, so the exponent is 3.

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

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

Example 3: Multiplying by Powers of 10 Find the value of each expression. A. 23.89  108 B. 467  10–3 C. 0.163  10-2 Move the decimal point 2 places to the left. Move the decimal point 8 places to the right. Move the decimal point 3 places to the left. 23.8 9 0 0 0 0 0 0 4 6 7 0.163 0.467 2,389,000,000 0.00163

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.

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.

Example 4: Converting to Scientific Notation Convert the following to scientific notation, if necessary. B. 985  106 C. 0.008  10-9 A. 15  103 Move the decimal point 1 place to the left. Add 1 to the exponent. Move the decimal point 2 places to the left. Add 2 to the exponent. Move the decimal point 3 places to the right. Minus 3 to the exponent. 1 5  103+1 9 8 5  106+2 .0 0 8  10-9-3 1.5  104 9.85  108 8  10-12

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. 1 2 0 0 0 0 Move the decimal point 5 places to the right. 120,000 km

Example 6: Astronomy Application Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km. Write Saturn’s distance from the Sun in scientific notation. Count the number of places you need to move the decimal point to get a number between 1 and 10. 1,427,000,000 1,4 2 7,0 0 0,0 0 0 9 places Use that number as the exponent of 10. 1.427  109 km