Algebra unit 7.1
27
UNIT 7.1 ZERO AND NEGATIVE UNIT 7.1 ZERO AND NEGATIVE EXPONENTS EXPONENTS
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Unit 7.1
Transcript of Algebra unit 7.1
UNIT 7.1 ZERO AND NEGATIVE UNIT 7.1 ZERO AND NEGATIVE EXPONENTSEXPONENTS
Warm UpEvaluate 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
Evaluate and multiply by powers of 10.Convert between standard notation and scientific notation.
Objectives
scientific notation
Vocabulary
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.
Find the value of each power of 10.
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
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 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.
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. 1,000
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
Find the value of each expression.
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 7
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 0 0 Move the decimal point 5 places to the right.
85,340,000
b. 0.163 × 10–2
0.0 0163
0.00163
Move the decimal point 2 places to the left.
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 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
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
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
1 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
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
Order the list of numbers from least to greatest.
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
Lesson Quiz: Part IFind 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
0.00293
3,745,000
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
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