Unit 4 – Number Patterns and Fractions
Lesson 5 – Converting between Fractions and Decimals
Blue – Converting between Fractions and Decimals
Complete
1. Since
7
7
= ____
= 0.7,
10
1000
2. Since
3
3
= ____
= 0.075,
40
400
3. Since
1
1
= ____
= 0.16,
6
60
4. Since
5
5
= ____
= 0.15,
33
330
Order the numbers from least to greatest.
5. 1.3, − 1.13, 1.03, − 1.30, −
7. −1.8, 0.18,
4
3
6. 0.06, 0.6, 0.60, 0.06, 0.606
21
6
, − 1.88, .18, 1.18,
18
5
8. a. Find the first three digits after the decimal in the expansion of 1/3.
b. How do we know that the decimal expansion of 1/3 repeats endlessly?
c. Find the repeating decimal expansions of the fractions 1/3, 2/3, and 10/3.
9. Critical Thinking. Try using calculator to find a decimal value for
1
. What do you
17
1
as a terminating or repeating decimal (go
17
out to 20 decimal digits). Explain the calculator result you obtained.
notice? Then use long division to write
Solutions
1. 0.007
2. 0.0075
3. 0.016
4. 0.015
5. −
4
, − 1.30, − 1.13, 1.03, 1.3
3
7. −1.8, − 1.88, .18, .18,
6. 0.06, 0.06, 0.60, 0.606, 0.6
21
6
, 1.18,
18
5
1
Unit 4 – Number Patterns and Fractions
Lesson 5 – Converting between Fractions and Decimals
8. We begin dividing 1 by 3 and see that the decimal expansion does not
terminate one, two, or even three digits past the decimal point. In
fact, at each step in the division process, we find ourselves dividing 3
into 10. The quotient is 3, which becomes a new digit of the decimal
of 1/3. The remainder is 1, to which we append a 0 and continue the
long division. Since this process never changes, the decimal
representation of 1/3 repeats endlessly. Follow the division yourself
and make sure you understand the repetition of division.
9. I do not see any repeating pattern of digits or any sign of termination;
0.0588235294117647; the calculator does not show enough decimal places for the
repeating pattern to appear, since the pattern has 16 digits.
2