Answer :
Answer:
one that has a finite number of digits
Step-by-step explanation:
A terminating decimal is one that has a finite number of digits. For example, 1/32 = 0.03125.
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A non-terminating decimal may be repeating or non-repeating. In the latter case, we call the number irrational. Square roots of non-square integers are irrational, for example. √2 = 1.41421356237309504880.... Their exact value cannot be represented by a decimal number.
If the decimal is repeating, it represents a rational number, one that can be written as the ratio of two integers. The length of repeat may be short or very long. For example, the decimal equivalent of the fraction 1/9 is 0.1111... (repeating). It is a single repeating digit. The decimal equivalent of the fraction 2/11 is 0.18181818... (repeating). It has a two-digit repeat.
For 1/7, the repeat length is 6 digits:
1/7 = 0.142857142857... (repeating)
In general, the repeat length may be up to n-1 digits for a fraction with a denominator of n.
The decimal equivalent of 1/17 has a 16-digit repeat, for example. 1/31 has a 30-digit repeat.
[tex]\dfrac{1}{17}=0.\overline{0588235294117647}[/tex]
When convenient, it is conventional to indicate the repeating digits with an overbar. Plain text makes that difficult, so the representation sometimes uses an underscore preceding the repeating digits: 1/7 = 0.142857_142857; or curly brackets around them: 3/13=0.230769{230769}.
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In the decimal number system, only fractions with denominators that are some product of powers of 2 and 5 will be terminating decimals.