Decimal Expansion of Rational Numbers: An Analysis

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Decimal Expansion of Rational Numbers: An Analysis Project 1.2 Decimal Expansion of Rational Numbers: An Analysis

Rational to Decimal When a rational number is converted to decimal, it is represented in the form p/q. In this form p/q = p(1/q). To determine which decimals will repeat or terminate, we need only investigate 1/q.

Determining those that Repeat When q is in the form of 2x5y and x and y are positive integers then 1/q will terminate . For all other values of q, 1/q will repeat. Values for which 1/q will terminate or repeat 1/1 Term. 1/11 Repeat 1/21 1/31 1/41 1/2 1/12 1/22 1/32 1/42 1/3 1/13 1/23 1/33 1/43 1/4 1/14 1/24 1/34 1/44 1/5 1/15 1/25 1/35 1/45 1/6 1/16 1/26 1/36 1/46 1/7 1/17 1/27 1/37 1/47 1/8 1/18 1/28 1/38 1/48 1/9 1/19 1/29 1/39 1/49 1/10 1/20 1/30 1/40 1/50

How to convert Repeating Decimal to Rational A terminating decimal can be easily displayed as a rational expression by multiplying the decimal by the inverse of the place value the end of the decimal occupies. A repeating decimal takes a little more work, but the place value still plays a vital role.

How to convert Repeating Decimal to Rational (continued) 1000r – r = 3132 Eg. 999r = 3132 and r = 3132/999 = 116/37 By multiplying the decimal by the place value inverse of the repeating point and manipulating the data as shown, it is possible to obtain a rational representation of the repeating decimal.