7-2 powers of 10 and scientific notation warm up warm up lesson presentation lesson presentation...

7-2 Powers of 10 and Scientific Notation

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7-2 Powers of 10 and Scientific NotationWarm UpEvaluate each expression.

1. 123 1,0002. 123 1,0003. 0.003 1004. 0.003 1005. 104

6. 10–4 7. 230

123,0000.1230.30.00003

10,0000.00011


2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

California Standards


scientific notationVocabulary

7-2 Powers of 10 and Scientific NotationThe 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.

7-2 Powers of 10 and Scientific NotationThe 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.


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


Find the value of each power of 10.

Additional Example 1: Evaluating Powers of 10

Start with 1 and move the decimal point six places to the left.

A. 10–6 C. 109 B. 104

1,000,000,000

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.

10,0000.000001

7-2 Powers of 10 and Scientific NotationCheck It Out! Example 1

Find the value of each power of 10.

a. 10–2 c. 1010 b. 105

10,000,000,000100,0000.01

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.


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

Reading Math


Write each number as a power of 10.

Additional Example 2: Writing Powers of 10

A. 1,000,000 The decimal point is six places to the right of 1, so the exponent is 6.

B. 0.0001 C. 1000 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.


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 product of any number and a power of 10. You start with the number instead of starting with 1.

Multiplying by Powers of 10


Find the value of each expression.

Additional Example 3: Multiplying by Powers of 10

A. 23.89 108

23.8 9 0 0 0 0 0 0

2,389,000,000

Move the decimal point 8 places to the right.

B. 467 10–3

4 6 70.467

Move the decimal point 3 places to the left.


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

0.0 01630.00163

Move the decimal point 2 places to the left.

7-2 Powers of 10 and Scientific NotationScientific 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.


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

Reading Math

7-2 Powers of 10 and Scientific NotationAdditional Example 4A: Astronomy ApplicationSaturn 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 0 120,000 km

Move the decimal point 5 places to the right.


Write Saturn’s distance from the Sun in scientific notation.

1,427,000,000

1,4 2 7,0 0 0,0 0 0

9 places

Additional Example 4B: Astronomy ApplicationSaturn 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. 1.427 109 km

7-2 Powers of 10 and Scientific NotationCheck It Out! Example 4a

Jupiter has a diameter of about 143,000 km. Write Jupiter’s diameter in scientific notation.

143,000 km1 4 3 0 0 0

5 places

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. 1.43 105 km

7-2 Powers of 10 and Scientific NotationCheck It Out! Example 4b

Jupiter’s orbital speed is approximately 1.3 × 104 m/s. 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

1.3 × 104 m/s


Order the list of numbers from least to greatest.

Additional Example 5: Comparing and Ordering Numbers in Scientific Notation

Step 1 List the numbers in order by powers of 10.

Step 2 Order the numbers that have the same power of 10.


Order the list of numbers from least to greatest.Check It Out! Example 5

Step 1 List the numbers in order by powers of 10.

Step 2 Order the numbers that have the same power of 10.

2 10-12, 4 10-3, 5.2 10-3, 3 1014, 4.5 1014, 4.5 1030

7-2 Powers of 10 and Scientific NotationLesson 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

0.002933,745,000

form.b. Write the volume of the Pacific Ocean in scientific notation. 1.7 108 mi3

7-2 Powers of 10 and Scientific NotationLesson Quiz: Part II

Find the value of each expression.4. Order the list of numbers from least to

greatest.

,

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