7-2 Powers of 10 and Scientific Notation Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1

Warm Up Evaluate each expression. 1. 123  1,000 2. 123  1,000 3. 0.003  100 4. 0.003  100 5. 104 6. 10–4 7. 230 123,000 0.123 0.3 0.00003 10,000 0.0001 1

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

Vocabulary scientific notation

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.

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

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

Check It Out! Example 1 Find the value of each power of 10. a. 10–2 b. 105 c. 1010 Start with 1 and move the decimal point two places to the left. Start with 1 and move the decimal point five places to the right. Start with 1 and move the decimal point ten places to the right. 0.01 100,000 10,000,000,000

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

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.

Check It Out! Example 2 Write each number as a power of 10. a. 100,000,000 b. 0.0001 c. 0.1 The decimal point is eight places to the right of 1, so the exponent is 8. The decimal point is four places to the left of 1, so the exponent is –4. The decimal point is one place to the left of 1, so the exponent is –1.

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 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

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

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

Check It Out! Example 4a 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

Example 5: Comparing and Ordering Numbers in Scientific Notation Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. Step 2 Order the numbers that have the same power of 10

Check It Out! Example 5 Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. 2  10-12, 4  10-3, 5.2  10-3, 3  1014, 4.5  1014, 4.5  1030 Step 2 Order the numbers that have the same power of 10

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

Lesson Quiz: Part II Find the value of each expression. 4. Order the list of numbers from least to greatest