### Algebra scientific notation

```Name ———————————————————————
SECTION
6
Date ————————————
Algebra
Lesson 4: Scientific Notation
Scientific notation is a way to write very small or very large numbers using
powers of 10. The table shows some powers of 10.
Power of 10
Value
10−2
10−1
100
101
102
103
0.001
0.01
0.1
1
10
100
1000
Write 9,100,000 in scientific notation.
HINT
Move the decimal point as
needed to get a number that
is at least 1, but less than 10.
9,100,000 Move the decimal point
6 places to the left.
9.1 3 106
EXAMPLE 2
Use 6 as an exponent of 10.
Write 0.0000005 in scientific notation.
HINT
Use positive exponents for
large numbers.
Use negative exponents for
small numbers.
0.0000005 Move the decimal point
7 places to the right.
5 3 10
−7
EXAMPLE 3
Use 27 as an exponent of 10.
6. ALGEBRA
4. Scientific Notation
EXAMPLE 1
10−3
Write 2.3 3 104 in standard form.
23,000
The exponent of 10 is 4.
Move the decimal point 4 places to the right.
EXAMPLE 4
Write 8 3 10−5 in standard form.
0.00008
The exponent of 10 is 25.
Move the decimal point 5 places to the left.
Practice: First Try
Write the power of 10 that makes a true statement.
1. 8,000,000 5 8 3 _____
2. 450,000 5 4.5 3 _____
3. 0.00006 5 6 3 _____
4. 0.000000077 5 7.7 3 _____
5. 380,000,000 5 3.8 3 _____
6. 0.00092 5 9.2 3 _____
McDougal Littell Middle School Math
Remediation Book Lesson 6.4
173
Name ———————————————————————
Date ————————————
Practice: Second Try
Write the number in scientific notation.
1. 87,000,000
2. 5,000,000,000
3.
4. 926,000
5. 0.0000015
6. 0.0000008
8. 0.000000398
9. 0.0000031
6. ALGEBRA
4. Scientific Notation
7.
0.0009
420,000
Write the number in standard form.
10. 5.9 3 106
11. 4.58 3 104
12. 9.0 3 102
13. 4 3 108
14. 7.5 31025
15. 8.2 3 1026
16. 1.82 3 1024
17. 3 3 1029
18. 5.5 3 1023
19. In the year 2005, a company made a profit of about \$3.8 3 105. In 2006, the
company made about \$40,000. In which year did the company make a greater
profit? Explain.
20. The size of Specimen A is 5 3 1024 cm. The size of Specimen B is 0.00055 cm.
Which specimen is smaller? Explain.
21. Explain why each number is not written in scientific notation.
a. 41 3 103
b. 0.3 3 1027
Puzzle
The mass of Earth is about 6 trillion trillion kilograms. Write this number!
Standard Notation
174
McDougal Littell Middle School Math
Remediation Book Lesson 6.4
Scientific Notation
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Name ———————————————————————
SECTION
6
Date ————————————
Algebra
Lesson 4: Scientific Notation
Scientific notation is a way to write very small or very large numbers using
powers of 10. The table shows some powers of 10.
Power of 10
Value
10−2
10−1
100
101
102
103
0.001
0.01
0.1
1
10
100
1000
Write 9,100,000 in scientific notation.
HINT
Move the decimal point as
needed to get a number that
is at least 1, but less than 10.
9,100,000 Move the decimal point
6 places to the left.
9.1 3 106
EXAMPLE 2
Use 6 as an exponent of 10.
Write 0.0000005 in scientific notation.
HINT
Use positive exponents for
large numbers.
Use negative exponents for
small numbers.
0.0000005 Move the decimal point
7 places to the right.
5 3 10
−7
EXAMPLE 3
Use 27 as an exponent of 10.
6. ALGEBRA
4. Scientific Notation
EXAMPLE 1
10−3
Write 2.3 3 104 in standard form.
23,000
The exponent of 10 is 4.
Move the decimal point 4 places to the right.
EXAMPLE 4
Write 8 3 10−5 in standard form.
0.00008
The exponent of 10 is 25.
Move the decimal point 5 places to the left.
Practice: First Try
Write the power of 10 that makes a true statement.
1. 8,000,000 5 8 3 _____
2. 450,000 5 4.5 3 _____
3. 0.00006 5 6 3 _____
4. 0.000000077 5 7.7 3 _____
5. 380,000,000 5 3.8 3 _____
6. 0.00092 5 9.2 3 _____
McDougal Littell Middle School Math
Remediation Book Lesson 6.4
173
Name ———————————————————————
Date ————————————
Practice: Second Try
Write the number in scientific notation.
1. 87,000,000
2. 5,000,000,000
3.
4. 926,000
5. 0.0000015
6. 0.0000008
8. 0.000000398
9. 0.0000031
6. ALGEBRA
4. Scientific Notation
7.
0.0009
420,000
Write the number in standard form.
10. 5.9 3 106
11. 4.58 3 104
12. 9.0 3 102
13. 4 3 108
14. 7.5 31025
15. 8.2 3 1026
16. 1.82 3 1024
17. 3 3 1029
18. 5.5 3 1023
19. In the year 2005, a company made a profit of about \$3.8 3 105. In 2006, the
company made about \$40,000. In which year did the company make a greater
profit? Explain.
20. The size of Specimen A is 5 3 1024 cm. The size of Specimen B is 0.00055 cm.
Which specimen is smaller? Explain.
21. Explain why each number is not written in scientific notation.
a. 41 3 103
b. 0.3 3 1027
Puzzle
The mass of Earth is about 6 trillion trillion kilograms. Write this number!
Standard Notation
174
McDougal Littell Middle School Math
Remediation Book Lesson 6.4
Scientific Notation