1. Scientific Notation
Lesson 5.2.3

2. Scientific Notation 5.2.3 California Standard: What it means for you:
Lesson
5.2.3
Scientific Notation
California Standard:
Number Sense 1.1
Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10), compare rational numbers in general.
What it means for you:
You’ll see how you can use powers of 10 to make very big or very small numbers easier to work with.
Key words:
scientific notation
numeric form
power
decimal
base
exponent

3. Lesson
5.2.3
Scientific Notation
Scientific notation is a handy way of writing very large and very small numbers. In an earlier lesson, you practiced using powers of ten to write out large numbers.
57,000,000 = 5.7 × 107
128,000,000,000 = 1.28 × 1011
In this Lesson, you’ll get a reminder of how to do that. Then you’ll see that with negative powers, you can do the same thing for very small numbers.

4. Lesson
5.2.3
Scientific Notation
You Can Use Powers of 10 to Write Large Numbers
In Chapter 2 you saw how to write large numbers as a product of two factors using scientific notation.
The first factor is a number that is at least 1 but less than 10.
1,200,000 = 1.2 × 106
The second factor is a power of ten. The exponent tells you how many places to move the decimal point to get the number.

5. Lesson
5.2.3
Scientific Notation
Example 1
The planet Saturn is about 880,000,000 miles away from the Sun. Write this number in scientific notation.
Solution
Split the number into the appropriate factors.
880,000,000 = 8.8 × 100,000,000
Write the power of ten in base and exponent form.
= 8.8 × 108 miles
Solution follows…

6. Scientific Notation 5.2.3 Guided Practice
Lesson
5.2.3
Scientific Notation
Guided Practice
Write the numbers in Exercises 1–6 in scientific notation.
1. 487,000,000,
3. 93,840, –1,630,000,000,000
5. 28,410,000,000, –3,854,000,000
4.87 × 1011
6 × 103
9.384 × 107
–1.63 × 1012
2.841 × 1013
–3.854 × 109
Solution follows…

7. Lesson
5.2.3
Scientific Notation
You Can Write Small Numbers in Scientific Notation
Scientific notation is also a useful way to write small numbers.
A number like can be rewritten as a division.
= 5.4 ÷ 1,000,000
= 5.4 ÷ 106
= 5.4 × 10–6
Using powers of 10 you can write this as 5.4 ÷ 106.
And remember that 1 ÷ 106 = = 10–6. 1
106
5.4 × 10–6 is written in scientific notation.

8. Lesson
5.2.3
Scientific Notation
Example 2
A red blood cell has a diameter of  m. Write this number in scientific notation.
Solution
Split the number into a decimal and a power of ten.
= 7 ÷ 1,000,000
Write the power of ten in base and exponent form.
= 7 ÷ 106
Change division by a positive power to multiplication by a negative power.
= 7 × 10–6 m
Solution follows…

9. Scientific Notation 5.2.3 Guided Practice
Lesson
5.2.3
Scientific Notation
Guided Practice
Write the numbers in Exercises 7–12 in scientific notation.
4.19 × 10–4
1.5 × 10–11
7 × 10–8
× 10–5
8.946 × 10–5
4.645 × 10–8
Solution follows…

10. Lesson
5.2.3
Scientific Notation
You Can Convert Numbers from Scientific Notation
Sometimes you might need to take a number that’s in scientific notation, and write it as an ordinary number.
When you multiply by 10, the decimal point moves one place to the right.
12.35 × 10 = 123.5
12.35 ÷ 10 = 1.235
When you divide by 10, the decimal point moves one place to the left.
You can use these facts to convert a number from scientific notation back to numeric form.

11. Scientific Notation 5.2.3 Write 3.0 × 1011 in numeric form. Solution
Lesson
5.2.3
Scientific Notation
Example 3
Write 3.0 × 1011 in numeric form.
Solution
“3.0 × 1011” means “multiply 3.0 by 10, 11 times.”
To multiply 3.0 by 1011, all you need to do is move the decimal point 11 places to the right.
It might help to write out the 3.0 with extra 0s — then you can see how the decimal point is moving.
3.0 × 1011 = × 1011
The green line shows the decimal point moving 11 places to the right. .
= 300,000,000,000
Solution follows…

12. Scientific Notation 5.2.3 Write 4.2 × 10–10 in numeric form. Solution
Lesson
5.2.3
Scientific Notation
Example 4
Write 4.2 × 10–10 in numeric form.
Solution
“4.2 × 10–10” means “divide 4.2 by 10, 10 times.”
You need to move the decimal point 10 places to the left.
You can write in extra 0s in front of the 4 to help you:
× 10–10 =
Solution follows…

13. Scientific Notation 5.2.3 Guided Practice
Lesson
5.2.3
Scientific Notation
Guided Practice
In Exercises 13–20, rewrite each number in numerical form.
× × 10–6
× × 10–8
× × 10–2
× × 10–5
5,910,000
2200
90,230,000
81,700,000,000
Solution follows…

14. Scientific Notation 5.2.3 Independent Practice
Lesson
5.2.3
Scientific Notation
Independent Practice
Write the numbers in Exercises 1–6 in scientific notation.
1. 78,
3. 843,000,000,
5. 20,057,000,000,000
7.8 × 104
9.1 × 10–7
8.43 × 1011
4.16 × 10–12
× 1013
× 10–22
Solution follows…

15. Scientific Notation 5.2.3 Independent Practice
Lesson
5.2.3
Scientific Notation
Independent Practice
Write the numbers in Exercises 7–12 in numerical form.
× × 10–5
× × 10–10
× × 10–3
80,000
2,180,000
5,050,500,000
Solution follows…

16. Scientific Notation 5.2.3 Independent Practice
Lesson
5.2.3
Scientific Notation
Independent Practice
13. The planet Uranus is approximately 1,800,000,000 miles away from the Sun. What is this distance in scientific notation?
14. An inch is approximately equal to miles. Write this distance in scientific notation.
15. The volume of the Earth is approximately 7.67 × 10–7 times the volume of the Sun. Express this figure in numeric form.
1.8 × 109 miles
1.58 × 10–5 miles
Solution follows…

17. Scientific Notation 5.2.3 Independent Practice
Lesson
5.2.3
Scientific Notation
Independent Practice
16. An electron's mass is approximately × 10–31 kg. What is this mass in numeric form?
17. In 2006, Congress approved a 69 billion dollar tax cut. What is 69 billion dollars written in scientific notation?
18. At the end of the 20th century, the world population was approximately 6.1 × 109 people. Express this population in numeric form. How would you say this number in words? kg
$6.9 × 1010
6,100,000,000 Six billion, one hundred million
Solution follows…

18. Scientific Notation 5.2.3 Round Up
Lesson
5.2.3
Scientific Notation
Round Up
Scientific notation is an important real-life use for powers — it’s called scientific notation because scientists use it all the time to save them having to write out really long numbers.