1. Thursday, Sept. 27

2. Fractions and Decimals
LESSON 2-6
Problem of the Day
(For help, go to Lesson 2-3.)
1. Vocabulary Review How can you tell whether fractions
are equivalent fractions?
Write two fractions equivalent to each fraction. 16 20 15 20 6 9 10 50
2-6

3. Fractions and Decimals
LESSON 2-6
Solutions
1. In simplest form, they are the same.
2–5. Answers may vary. Samples are given. 3. 4 5 , 8 10 3 4 , 6 8 2 3 , 8 12 1 5 , 2 10
2-6

4. Fractions and Decimals
LESSON 2-6
Additional Examples
The total amount of rainfall yesterday was reported as in.
Express the amount of rainfall as a decimal. 1 4
or 1 ÷ 4 = 1 4
0.25 –8 20
–20
quotient
The remainder
is 0.
So, = The total amount of rainfall was 0.25 in. 1 4
2-6

5. Fractions and Decimals
LESSON 2-6
Additional Examples 7 15
Write as a decimal.
The digit “6” repeats.
There will always
be a remainder.
or 7 ÷ 15 =
0.4666
–60
100
–90 7 15 10 7 15
So, = 0.46.
2-6

6. Fractions and Decimals
LESSON 2-6
Additional Examples
Write as a fraction in simplest form.
Since = , =
105
1,000
= 4
105
1,000
105 ÷ 5
1,000 ÷ 5
Use the GCF to write the fraction in simplest form.
= 4 21
200
2-6

7. Fractions and Decimals
LESSON 2-6
Additional Examples
Order from least to greatest: 3 4 7 10 3
, 2.897, 3 3 4
= 3.75
Convert fractions
to decimals. 7 10 3
= 3.70
2.897, 3.70, 3.75 , 3
2.897, 7 10 4
Order from least to greatest.
2-6

8. Fractions and Decimals
LESSON 2-6
Additional Examples
In a survey of next year’s seventh-grade students, 0.25 said
they will come to school by bus, said they will walk, said
they will come in a car, and said they will ride their bicycles. Order
the means of transportation from most used to least used. 5 24 1 16
bicycles 1 16 =
Change the fractions to decimals.
walk 5 24 =
Since > 0.25 > > , the means of transportation are car, bus, walking, and bicycle.
2-6

9. Fractions and Decimals
LESSON 2-6
Practice
Write each fraction as a decimal.
1. 2.
3. 4. 7 8 4 9
0.875
0.4 3 5 5 16
0.6
0.3125
2-6

10. Homework for Thursday, Sept. 27
Practice 2-6
Quiz on Saturday - Lessons 2-1 to 2-4

11. Friday, Sept. 28

12. Rational Numbers
LESSON 2-7
Problem of the Day
(For help, go to Lesson 2-6.)
1. Vocabulary Review Is a repeating decimal or a
terminating decimal? Explain.
Write each fraction as a decimal. 3 4 7 9 1 3 12 48 –
2-7

13. 1.Terminating decimal; the decimal stops.
Rational Numbers
LESSON 2-7
Solutions
1.Terminating decimal; the decimal stops.
–0.7
2-7

14. Rational Numbers
LESSON 2-7
Additional Examples
Compare – and – . 1 4 3 8
Method 1
Since – is farther to the left on the number line, it is the lesser number. 3 8
So, – > – . 1 4 3 8
2-7

15. Rewrite – with a –1 in the numerator.
Rational Numbers
LESSON 2-7
Additional Examples
(continued)
Method 2
– = 1 4 –1
Rewrite – with a –1 in the numerator.
The LCD is 8. Write an equivalent fraction. =
–1  2
4  2
The fraction – is equivalent to . 2 8 = –2
= –
Since – > – , then – > – . 2 8 3 1 4
2-7

16. Compare. Use <, >, or =.
Rational Numbers
LESSON 2-7
Additional Examples
Compare. Use <, >, or =.
a and 8.1
8.7 > 8.1
Both numbers are positive. Compare the digits.
b. –8.7 and 8.1
–8.7 < 8.1
Any negative number is less than a positive number.
c. –8.7 and –8.1
–8.7 < –8.1
Place the decimals on a number line and compare their locations.
2-7

17. Order these numbers from least to greatest:
Rational Numbers
LESSON 2-7
Additional Examples
Order these numbers from least to greatest:
– , 0.625, , –0.5 3 5 2 3 5
– = –3 ÷ 5 = –0.6
Write as a decimal.
Write as a repeating decimal. 2 3
= 2 ÷ 3 = 0.6
Compare the decimals.
–0.6 < –0.5 < < 0.6
From least to greatest, the numbers are – , –0.5, 0.625, . 3 5 2
2-7

18. Practice Compare. Use <, >, or =. 1. – 2. –
Rational Numbers
LESSON 2-7
Practice
Compare. Use <, >, or =.
1. – 2. –
– – –8.6 3 4 4 7 1 8 3 8
< –
> –
>
<
2-7

19. Homework for Friday, Sept. 28
(in HW Notebooks)
Lesson 2-7, p , #s 8-30 evens, #31
Quiz tomorrow - Lessons 2-1 to 2-4

20. Saturday, Sept. 29
Quiz on Lessons 2-1 to 2-4

21. Problem of the Day 1. Vocabulary Review An exponent tells you how many
Scientific Notation
LESSON 2-8
Problem of the Day
(For help, go to Lesson 2-1.)
1. Vocabulary Review An exponent tells you how many
times a number, or base, is used as a ? .
Simplify.
2-8

22. Solutions 1. factor 2. 33 = 3 • 3 • 3 = 27 3. 42 = 4 • 4 = 16
Scientific Notation
LESSON 2-8
Check Skills You’ll Need
Solutions
1. factor
2. 33 = 3 • 3 • 3 = 27
3. 42 = 4 • 4 = 16
= 10 • 10 • 10 • 10 • 10 = 100,000
= 2 • 2 • 2 • 2 = 16
2-8

23. Write as a product of 2 factors.
Scientific Notation
LESSON 2-8
Additional Examples
Quick Check
The mean distance from Mars to the sun is about 141,750,000 mi. Write this number in scientific notation.
Move the decimal point to get a factor greater than 1 but less than 10.
1. 41,750,000.
141,750,000 =  100,000,000
Write as a product of 2 factors.
=  108
Write 100,000,000 as a power of 10.
The mean distance from Mars to the sun is about  108 mi.
2-8

24. Write as a product of 2 factors.
Scientific Notation
LESSON 2-8
Additional Examples
Light from the sun reaches Earth in about  102 s. Write this time in standard form.
Method 1
 102 =  100
Write as a product of 2 factors. =
Multiply the factors.
Method 2
 102 =
The exponent is 2. Move the
decimal 2 places to the right. =
The time is about s.
2-8

25. Practice Write in scientific notation. 1. 45,300 2. 714,900,000
LESSON 2-8
Practice
Write in scientific notation.
1. 45, ,900,000
Write in standard form.
  106
4.53  104
7.149  108
5,700
6,034,000
2-8

26. Homework for Saturday, Sept. 29
(in HW Notebooks)
Lesson 2-8, p , #s evens, #34