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Math 205
Test 2 Key
Instructions
1. Do NOT write your answers on these sheets. Nothing written on the test papers will be graded.
2. Please begin each section of questions on a new sheet of paper.
3. Please do not write answers side by side.
4. Please do not staple your test papers together.
5. Limited credit will be given for incomplete or incorrect justification.
Questions
1. Arithmetic with repeating decimals
(a) Example 1
i. (3) Convert
1
9
,
1
11
,
20
99
to decimal.
0.1111
9 1.0000
9
10
9
10
9
10
9
1
0.0909
11 1.0000
99
100
99
1
0. 2 0 2
99 20.000
198
200
198
2
ii. (2) Add
1
9
+
1
11
as fractions.
1
9
+
1
11
= we change to a common denominator
1
9
·
11
11
+
1
11
·
9
9
=
11
99
+
9
99
= with the common denominator we add
20
99
.
iii. (3) Add
1
9
+
1
11
as decimals. Use the same addition algorithm used for non-repeating decimals.
0.1111
0.0909
0.2020
iv. (1) Do your two answers match?
Yes. Based on the calculations above...

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