Objectives Convert between standard notation and scientific notation

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

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

Example 3: Multiplying by Powers of 10 Find the value of each expression. A. 23. 89 108 23. 8 9 0 0 0 2, 389, 000 Move the decimal point 8 places to the right. B. 467 10– 3 467 0. 467 Move the decimal point 3 places to the left.

Check It Out! Example 3 Find the value of each expression. a. 853. 4 105 853. 4 0 0 85, 340, 000 Move the decimal point 5 places to the right. b. 0. 163 10– 2 0. 0 0163 0. 00163 Move the decimal point 2 places to the left.

Example 4 A: Astronomy Application Saturn has a diameter of about Its distance from the Sun is about 1, 427, 000 km. Write Saturn’s diameter in standard form. 120000 120, 000 km Move the decimal point 5 places to the right.

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

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

Example 1 Use the information above to write Jupiter’s diameter in scientific notation. 143, 000 km 143000 5 places 1. 43 105 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.

Check It Out! Example 4 b Use the information above to write Jupiter’s orbital speed in standard form. 13000 13, 000 m/s Move the decimal point 4 places to the right.

Lesson Quiz: Part I Find the value of each expression. 1. 3, 745, 000 2. 0. 00293 3. The Pacific Ocean has an area of about 6. 4 х 107 square miles. Its volume is about 170, 000 cubic miles. a. Write the area of the Pacific Ocean in standard form. b. Write the volume of the Pacific Ocean in scientific notation. 1. 7 108 mi 3