Question
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
Step 1
From the explanation, we know that these are $\frac{13}{3125}$, $\frac{17}{8}$, $\frac{15}{1600}$, $\frac{23}{125}$, $\frac{65}{125}$, and $\frac{35}{50}$. Show more…
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The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form $\frac{p}{q}$, what can you say about the prime factors of $q$ ? (i) $43.123456789$ (ii) $0.120120012000120000 \ldots$ (iii) $43 . \overline{123456789}$
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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: (i) $\frac{13}{3125}$ (ii) $\frac{17}{8}$ (iii) $\frac{64}{455}$ (iv) $\frac{15}{1600}$ (v) $\frac{29}{343}$ (vi) $\frac{23}{2^{3} 5^{2}}$ (vii) $\frac{129}{2^{2} 5^{7} 7^{5}}$ (viii) $\frac{6}{15}$ (ix) $\frac{35}{50}$ (x) $\frac{77}{210}$
Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal. Then classify the number as a rational number or as an irrational number. (see Example 2) $$\frac{1}{5}$$
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