Rational Numbers, Decimals, Geometric Series, Approximations
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1
2Rational Numbers, Decimals, Geometric Series, Approximations
1. Circle each rational number.
2
3
22
,
,
0,
2,
3,
2,
3.14,
,
π
5
4
7
2. Rewrite the following quantities in decimal form.
3
5
(a)
+
100
10000
4
3
(b)
+
3
4
10
10
4
3
6
(c) 10
+
4
9
10
10
3. Find the decimal representation for the following numbers. If you obtain a repeating decimal, be
sure to clearly show which digits repeat.
1
2
5
3
4
3
3
8
3
6
16
9
80
7
4. The repeating decimal 0.45981 = 0.459818181 . . . has a period of length 2 since 81 repeats. One
might be tempted to say that the period could also be 4 since 8181 repeats. However for the period
we always look at the smallest repeating part. Without converting to decimal form, determine
the maximum length of the period for the following fractions. It will be helpful to think about
the possible remainders obtained when doing long division.
5
(a)
17
2
(b)
37
6
(c)
13
5. Explain precisely when a fraction can be represented by a terminating decimal.
6. Which of the following numbers can be represented by a terminating decimal. You should not
have to determine the decimal form in order to answer this question.
4
6
17
7
3
21
19
81
7
3
2
4
2
3
7
2
8
80
48
2
5
10
2
5
7
2
3
5
2
3
1
7. What is the sum of the finite geometric series a + ar + ar
+ ar
+
+ ar
+ ar ? Are there
any conditions which must be true in order for this sum to be valid?
2
3
8. What is the sum of the infinite geometric series a + ar + ar
+ ar
+
? Are there any conditions
which must be true in order for this sum to be valid?
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