4-1 Terminating and Repeating Decimals
Write the fraction or mixed number as a decimal. Use bar notation if needed.
1. SOLUTION: Think:
= 0.5.
So,
ANSWER: 0.5
2. SOLUTION: Think of the mixed number as a sum. Write the mixed number without the negative sign.
Write
as a decimal.
Think:
So,
= 0.16.
Add the negative sign.
So,
= –4.16.
ANSWER: –4.16
3. SOLUTION: eSolutions Manual - Powered by Cognero
So,
= 0.125.
Page 1
= –4.16.
So,
ANSWER: and Repeating Decimals
4-1 Terminating
–4.16
3. SOLUTION: So,
= 0.125.
ANSWER: 0.125
4. SOLUTION: So,
= 0.1875.
ANSWER: 0.1875
5. SOLUTION: Think:
So,
= –0.66.
ANSWER: –0.66
eSolutions Manual - Powered by Cognero
Page 2
So,
= 0.1875.
ANSWER: and Repeating Decimals
4-1 Terminating
0.1875
5. SOLUTION: Think:
So,
= –0.66.
ANSWER: –0.66
6. SOLUTION: So,
= –0.425.
ANSWER: –0.425
7. SOLUTION: Think of the mixed number as a sum.
Write
as a decimal.
eSolutions
- Powered by Cognero
So, Manual
= 0.875.
Page 3
So,
= –0.425.
ANSWER: and Repeating Decimals
4-1 Terminating
–0.425
7. SOLUTION: Think of the mixed number as a sum.
Write
So,
So,
as a decimal.
= 0.875.
= 5.875.
ANSWER: 5.875
8. SOLUTION: Think of the mixed number as a sum.
Write
as a decimal.
eSolutions Manual - Powered by Cognero
So,
= 0.375.
Page 4
So,
= 5.875.
ANSWER: and Repeating Decimals
4-1 Terminating
5.875
8. SOLUTION: Think of the mixed number as a sum.
Write
So,
So,
as a decimal.
= 0.375.
= 9.375.
ANSWER: 9.375
9. SOLUTION: So,
.
ANSWER: eSolutions Manual - Powered by Cognero
10. Page 5
So,
= 9.375.
ANSWER: and Repeating Decimals
4-1 Terminating
9.375
9. SOLUTION: So,
.
ANSWER: 10. SOLUTION: So,
.
ANSWER: 11. SOLUTION: eSolutions Manual - Powered by Cognero
Page 6
So,
.
ANSWER: 4-1 Terminating and Repeating Decimals
11. SOLUTION: So,
.
ANSWER: 12. SOLUTION: Think of the mixed number as a sum.
Write
So,
as a decimal.
.
eSolutions Manual - Powered by Cognero
So,
.
Page 7
So,
.
ANSWER: 4-1 Terminating and Repeating Decimals
12. SOLUTION: Think of the mixed number as a sum.
Write
as a decimal.
So,
.
So,
.
ANSWER: Write the decimal as a fraction or mixed number in simplest form.
13. –0.2
SOLUTION: The final digit, 2, is in the tenths place.
So, –0.2 =
.
ANSWER: eSolutions Manual - Powered by Cognero
14. 0.55
SOLUTION: Page 8
So,
.
ANSWER: 4-1 Terminating and Repeating Decimals
Write the decimal as a fraction or mixed number in simplest form.
13. –0.2
SOLUTION: The final digit, 2, is in the tenths place.
So, –0.2 =
.
ANSWER: 14. 0.55
SOLUTION: The final digit, 5, is in the hundredths place.
So, 0.55 =
.
ANSWER: 15. 5.96
SOLUTION: Think of the decimal as a sum.
5.96 = 5 + 0.96
Write 0.96 as a fraction.
The final digit, 6, is in the hundredths place.
So, 0.96 =
.
eSolutions Manual - Powered by Cognero
So, 5.96 =
.
Page 9
ANSWER: 4-1 Terminating and Repeating Decimals
15. 5.96
SOLUTION: Think of the decimal as a sum.
5.96 = 5 + 0.96
Write 0.96 as a fraction.
The final digit, 6, is in the hundredths place.
So, 0.96 =
.
So, 5.96 =
.
ANSWER: 16. The screen on Brianna’s new phone is 2.85 centimeters long. What mixed number represents the length of the
phone screen?
SOLUTION: Think of the decimal as a sum.
2.85 = 2 + 0.85
Write 0.85 as a fraction.
The final digit, 5, is in the hundredths place.
So, 0.85 =
So,
.
represents this length.
ANSWER: eSolutions Manual - Powered by Cognero
17. Page 10
praying mantis is an interesting insect that can rotate its head 180 degrees. Suppose a praying mantis is
10.5 centimeters long. What mixed number represents this length?
ANSWER: 4-1 Terminating and Repeating Decimals
16. The screen on Brianna’s new phone is 2.85 centimeters long. What mixed number represents the length of the
phone screen?
SOLUTION: Think of the decimal as a sum.
2.85 = 2 + 0.85
Write 0.85 as a fraction.
The final digit, 5, is in the hundredths place.
So, 0.85 =
So,
.
represents this length.
ANSWER: 17. praying mantis is an interesting insect that can rotate its head 180 degrees. Suppose a praying mantis is
10.5 centimeters long. What mixed number represents this length?
SOLUTION: Think of the decimal as a sum.
10.5 = 10 + 0.5
Write 0.5 as a fraction.
The final digit, 5, is in the tenths place.
So, 0.5 = .
So, 10 represents this length.
ANSWER: Problems
18. Persevere
eSolutions
Manual - with
Powered
by CogneroSuppose
you buy a 1.25-pound package of ham at $5.20 per pound. a. What fraction of a pound did you buy?
Page 11
So, 10 represents this length.
ANSWER: 4-1 Terminating and Repeating Decimals
18. Persevere with Problems Suppose you buy a 1.25-pound package of ham at $5.20 per pound. a. What fraction of a pound did you buy?
b. How much money did you spend?
SOLUTION: a.
Think of the decimal as a sum.
1.25 = 1 + 0.25
Write 0.25 as a fraction.
The final digit, 5, is in the hundredths place.
So, 0.25 =
.
The fraction of a pound you bought is
or .
b.
Multiply.
So you spent $6.50
ANSWER: a.
or
b.
$6.50
19. Identify Structure Write a fraction that is equivalent to a terminating decimal between 0.5 and 0.75.
SOLUTION: Think of a decimal value between 0.5 and 0.75.
Sample answer: One terminating decimal that is between 0.5 and 0.75 is 0.6. Change 0.6 to a fraction.
The final digit, 6, is in the tenths place.
eSolutions Manual - Powered by Cognero
So, 0.6 =
.
Page 12
a.
or
4-1 Terminating
and Repeating Decimals
b.
$6.50
19. Identify Structure Write a fraction that is equivalent to a terminating decimal between 0.5 and 0.75.
SOLUTION: Think of a decimal value between 0.5 and 0.75.
Sample answer: One terminating decimal that is between 0.5 and 0.75 is 0.6. Change 0.6 to a fraction.
The final digit, 6, is in the tenths place.
So, 0.6 =
.
ANSWER: Sample answer:
20. Persevere with Problems Fractions in simplest form that have denominators of 2, 4, 8, 16, and 32 produce terminating decimals. Fractions with denominators of 6, 12, 18, and 24 produce repeating decimals. What causes the
difference? Explain.
SOLUTION: Sample answer: Write the prime factorization of the first set of numbers.
2=2
4 = 2 × 2
8 = 2 × 2 × 2
16 = 2 × 2 × 2 × 2
32 = 2 × 2 × 2 × 2 × 2
Write the prime factorization of the second set of numbers.
6 = 2 × 3
12 = 2 × 2 × 3
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
The first set of numbers can be factored into primes of 2s. The second set of numbers can be factored into primes of
2s and 3s; the factor of 3 produces the repeating decimal.
ANSWER: Sample answer: The first set of numbers can be factored into primes of 2s. The second set of numbers can be
factored into primes of 2s and 3s; the factor of 3 produces the repeating decimal.
21. Persevere with Problems The value of pi (π) is 3.1415926… . The mathematician Archimedes believed that π was between
and . Was Archimedes correct? Explain your reasoning.
SOLUTION: Sample answer: Write the mixed numbers as decimals. Think of the mixed number as a sum.
Write
as a decimal.
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Page 13
Think of the mixed number as a sum.
4-1 Terminating and Repeating Decimals
Write as a decimal.
So,
.
Think of the mixed number as a sum.
Write
So,
as a decimal.
.
eSolutions Manual - Powered by Cognero
Page 14
4-1 Terminating and Repeating Decimals
So,
.
So,
≈ 3.14286 and ≈ 3.14085; Since 3.1415927... is between and , Archimedes was correct.
ANSWER: Sample answer:
≈ 3.14286 and ≈ 3.14085; Since 3.1415927... is between and , Archimedes was
correct.
22. Reason Inductively A unit fraction is a fraction that has 1 as its numerator. Write the four greatest unit fractions
that are repeating decimals. Then write each fraction as a decimal.
SOLUTION: The smaller the denominator, the larger the fraction. Of the first 10 numbers, fractions with a denominator of 1, 2, 4,
5, 8, and 10 all terminate. That leaves 3, 6, 7, and 9 as denominators. Divide each fraction to determine the decimal.
For : So,
.
For : So,
.
For : eSolutions Manual - Powered by Cognero
Page 15
So,
.
4-1 Terminating and Repeating Decimals
For : So,
.
For : So,
.
ANSWER: 23. Model with Mathematics Write a real-world scenario in which it would be appropriate to write a value in fraction
form.
SOLUTION: Sample answer: Jason was building a cabin. He cut a board to the length of
feet long.
ANSWER: Sample answer: Jason was building a cabin. He cut a board to the length of
feet long.
Write the fraction or mixed number as a decimal. Use bar notation if needed.
24. SOLUTION: eSolutions Manual - Powered by Cognero
Think:
Page 16
Sample answer: Jason was building a cabin. He cut a board to the length of
feet long.
ANSWER: 4-1 Terminating and Repeating Decimals
Sample answer: Jason was building a cabin. He cut a board to the length of
feet long.
Write the fraction or mixed number as a decimal. Use bar notation if needed.
24. SOLUTION: Think:
So,
= 0.8.
ANSWER: 0.8
25. SOLUTION: Think of the mixed number as a sum. Write the mixed number without the negative sign.
Write
as a decimal.
Think:
So,
= 0.05.
Add the negative sign.
So,
= –7.05.
ANSWER: –7.05
26. SOLUTION: eSolutions Manual - Powered by Cognero
So,
.
Page 17
So,
= –7.05.
ANSWER: and Repeating Decimals
4-1 Terminating
–7.05
26. SOLUTION: So,
.
ANSWER: 27. SOLUTION: Think of the mixed number as a sum.
Write
So,
So,
as a decimal.
.
.
ANSWER: eSolutions Manual - Powered by Cognero
28. The fraction of a dime that is made up of copper is
Page 18
. Write this fraction as a decimal.
So,
.
ANSWER: 4-1 Terminating and Repeating Decimals
27. SOLUTION: Think of the mixed number as a sum.
Write
So,
So,
as a decimal.
.
.
ANSWER: 28. The fraction of a dime that is made up of copper is
. Write this fraction as a decimal.
SOLUTION: So,
is 0.75.
ANSWER: 0.75
Write the decimal as a fraction or mixed number in simplest form.
29. –0.9Manual - Powered by Cognero
eSolutions
SOLUTION: The final digit, 9, is in the tenths place.
Page 19
So,
is 0.75.
ANSWER: and Repeating Decimals
4-1 Terminating
0.75
Write the decimal as a fraction or mixed number in simplest form.
29. –0.9
SOLUTION: The final digit, 9, is in the tenths place.
So, –0.9 =
.
ANSWER: 30. 0.34
SOLUTION: The final digit, 4, is in the hundredths place.
So, 0.34 =
.
ANSWER: 31. 2.66
SOLUTION: Think of the decimal as a sum.
2.66 = 2 + 0.66
Write 0.66 as a fraction.
The final digit, 6, is in the hundredths place.
So, 0.66 =
So, 2.66 =
.
.
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ANSWER: Page 20
ANSWER: 4-1 Terminating and Repeating Decimals
31. 2.66
SOLUTION: Think of the decimal as a sum.
2.66 = 2 + 0.66
Write 0.66 as a fraction.
The final digit, 6, is in the hundredths place.
So, 0.66 =
.
So, 2.66 =
.
ANSWER: Write the following as an improper fraction.
32. –13
SOLUTION: ANSWER: 33. SOLUTION: Think of the mixed number as a sum.
There are 7 × 3, or 21 thirds in the whole number 7. The sum of 21 thirds and one third is 22 thirds.
So,
.
ANSWER: eSolutions Manual - Powered by Cognero
34. –3.2
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ANSWER: 4-1 Terminating and Repeating Decimals
33. SOLUTION: Think of the mixed number as a sum.
There are 7 × 3, or 21 thirds in the whole number 7. The sum of 21 thirds and one third is 22 thirds.
So,
.
ANSWER: 34. –3.2
SOLUTION: The final digit, 2, is in the tenths place.
So, –3.2 =
.
ANSWER: 35. Be Precise Nicolás practiced playing the cello for 2 hours and 18 minutes. Write the time Nicolás spent practicing as a decimal.
SOLUTION: Because there are 60 minutes in one hour, 2 hours and 18 minutes can be represented by the mixed number
, or
.
Think of the mixed number as a sum.
Write
as a decimal.
Think:
eSolutions
Manual - Powered by Cognero
So, Nicolás practiced for 2.3 hours.
ANSWER: Page 22
ANSWER: 4-1 Terminating and Repeating Decimals
35. Be Precise Nicolás practiced playing the cello for 2 hours and 18 minutes. Write the time Nicolás spent practicing as a decimal.
SOLUTION: Because there are 60 minutes in one hour, 2 hours and 18 minutes can be represented by the mixed number
, or
.
Think of the mixed number as a sum.
Write
as a decimal.
Think:
So, Nicolás practiced for 2.3 hours.
ANSWER: 2.3 h
36. The table shows the lengths of four hiking trails. Select the appropriate decimal equivalent of each trail length.
SOLUTION: Write the fraction corresponding to each hiking trail as a decimal.
Lakeview: Think of the mixed number as a sum.
You know that
So,
.
.
eSolutions Manual - Powered by Cognero
Forest Lane: Think of the mixed number as a sum. Page 23
You know that
.
4-1 Terminating and Repeating Decimals
So,
.
Forest Lane: Think of the mixed number as a sum. Write
So,
So,
as a decimal.
.
.
Sparrow Stroll: Think of the mixed number as a sum.
Write
So,
So,
as a decimal.
.
.
Mountain Climb: Think of the mixed number as a sum. Write
as a decimal.
eSolutions Manual - Powered by Cognero
Page 24
So,
.
Mountain Climb: Think of the mixed number as a sum. 4-1 Terminating and Repeating Decimals
Write as a decimal.
So,
.
So,
.
ANSWER: 37. Zoe went to lunch with a friend. After tax, her bill was $12.05. Which of the following rational numbers is equivalent
to this amount? Select all that apply.
SOLUTION: Determine if each rational number is the same as 12.05 by changing it's form.
For
:
The final digit, 5, is in the hundredths place. Write 12.05 as mixed number with a denominator of 100. Then simplify.
eSolutions Manual - Powered by Cognero
So, 12.05 =
.
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4-1 Terminating and Repeating Decimals
37. Zoe went to lunch with a friend. After tax, her bill was $12.05. Which of the following rational numbers is equivalent
to this amount? Select all that apply.
SOLUTION: Determine if each rational number is the same as 12.05 by changing it's form.
For
:
The final digit, 5, is in the hundredths place. Write 12.05 as mixed number with a denominator of 100. Then simplify.
So, 12.05 =
.
For
:
Change
For
, so
is not equivalent.
:
Change
into an improper fraction:
20 ×12 + 1 = 241, so For . into a mixed number, which is
. Therefore, these are equivalent.
:
Simplify
:
So, these are equivalent. ANSWER: Round the decimal to the tenths place.
38. 5.69
SOLUTION: eSolutions
Manual - Powered by Cognero
The number to the right of the tenths place is 5. Since 9 ≥ 5 the 6 in the tenths place is rounded up to 7. So, 5.69 ≈ 5.7.
Page 26
ANSWER: 4-1 Terminating and Repeating Decimals
Round the decimal to the tenths place.
38. 5.69
SOLUTION: The number to the right of the tenths place is 5. Since 9 ≥ 5 the 6 in the tenths place is rounded up to 7. So, 5.69 ≈ 5.7.
ANSWER: 5.7
39. 0.05
SOLUTION: The number to the right of the tenths place is 5. Since 5 ≥ 5 the 0 in the tenths place is rounded up to 1. So, 0.05 ≈ 0.1.
ANSWER: 0.1
40. 98.99
SOLUTION: The number to the right of the tenths place is 9. Since 9 ≥ 5 the 9 in the tenths place is rounded up which changes the next place value. So, 98.99 ≈ 99.0.
ANSWER: 99.0
Graph and label the fraction on the number line below.
41. SOLUTION: There are 12 intervals on the number line between 0 and 1. Find an equivalent fraction to
12.
with a denominator of
Place a dot on the 6th hash mark from 0 on the number line and label it.
ANSWER: 42. eSolutions Manual - Powered by Cognero
SOLUTION: There are 12 intervals on the number line between 0 and 1. Find an equivalent fraction to
Page 27
with a denominator of
4-1 Terminating and Repeating Decimals
42. SOLUTION: There are 12 intervals on the number line between 0 and 1. Find an equivalent fraction to
12.
with a denominator of
Place a dot on the 9th hash mark from 0 on the number line and label it.
ANSWER: 43. SOLUTION: There are 12 intervals on the number line between 0 and 1. Find an equivalent fraction to
12.
with a denominator of
Place a dot on the 8th hash mark from 0 on the number line and label it.
ANSWER: 44. The table shows the discount on athletic shoes at two stores selling sporting equipment. Which store is offering the
greater discount? Explain.
SOLUTION: Write each number as a decimal.
25% =
= 0.25
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Manual - Powered by Cognero
Since 0.25 > 0.20, 25% > ANSWER: Page 28
ANSWER: 4-1 Terminating and Repeating Decimals
44. The table shows the discount on athletic shoes at two stores selling sporting equipment. Which store is offering the
greater discount? Explain.
SOLUTION: Write each number as a decimal.
25% =
= 0.25
Since 0.25 > 0.20, 25% > ANSWER: Go Time; Sample answer:
eSolutions Manual - Powered by Cognero
= 0.20 and 25% = 0.25; Since 0.25 > 0.20, 25% > .
Page 29