Objectives Convert between standard notation and scientific notation.

Scientific notation is a method of writing numbers that are very large or very small. The first part is a number that is greater than or equal to 1 and less than 10. The second part is a power of 10.

Multiplying by Powers of 10

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 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

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

Check It Out! Example 3 Find the value of each expression. a. 853.4  105 853.4 0 0 0 0 Move the decimal point 5 places to the right. 85,340,000 b. 0.163  10–2 Move the decimal point 2 places to the left. 0.0 0163 0.00163

Example 4A: 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 4B: 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

Standard form refers to the usual way that numbers are written—not in scientific notation. Reading Math

Example 1 Use the information above to write Jupiter’s diameter in scientific notation. 143,000 km Count the number of places you need to move the decimal point to get a number between 1 and 10. 1 4 3 0 0 0 5 places Use that number as the exponent of 10. 1.43  105 km

Check It Out! Example 4b Use the information above to write Jupiter’s orbital speed in standard form. 1 3 0 0 0 Move the decimal point 4 places to the right. 13,000 m/s

Lesson Quiz: Part I Find the value of each expression. 1. 2. 3. The Pacific Ocean has an area of about 6.4 х 107 square miles. Its volume is about 170,000,000 cubic miles. a. Write the area of the Pacific Ocean in standard 3,745,000 0.00293 form. b. Write the volume of the Pacific Ocean in scientific notation. 1.7  108 mi3