Which of these fractions are terminating decimals?A. \(\frac { 9} { 20} \) B. \(\frac { 1} { 35} \) C. \(\frac { 14} { 35} \) D. \(\frac { 1} { 16} \)

1. Identify the condition for a fraction to be a terminating decimal: 
A fraction \(\frac { a} { b} \) is a terminating decimal if and only if the denominator \(b\) (in its simplest form) has only the prime factors 2 and/or 5.

2. Check each fraction:

A. \(\frac { 9} { 20} \): Simplify the denominator \(20 = 2^ 2 \times 5\). Only prime factors are 2 and 5.  

B. \(\frac { 1} { 35} \): Simplify the denominator \(35 = 5 \times 7\). Contains prime factor 7. 

C. \(\frac { 14} { 35} \): Simplify the fraction to \(\frac { 2} { 5} \). The denominator \(5\) contains only the prime factor 5.

D. \(\frac { 1} { 16} \): Simplify the denominator \(16 = 2^ 4\). Only prime factor is 2. 

Supplemental Knowledge:

A fraction can be expressed as a terminating decimal if its denominator, when reduced to its simplest form, has only the prime factors 2 and/or 5. This is because a fraction in its simplest form can be written as \(\frac { a} { b} \), where \(b\) must be of the form \(2^ m \times 5^ n\) for some non-negative integers \(m\) and \(n\).

Real-Life Connections:

Knowledge of whether a fraction yields an indeceasing or decreasing decimal has practical applications in fields like finance and engineering where precise calculations are essential.
Assume you're an engineer designing components which must fit together perfectly, using measurements with terminating decimals ensures your calculations are precise, decreasing any risks during manufacturing.

Mastering concepts like identifying terminating decimals is essential for anyone involved in fields requiring precise mathematical calculations. At UpStudy, we offer comprehensive resources designed to enhance your understanding of these critical elements, including a Fractions calculator.

For those looking to deepen their knowledge in mathematics or seeking assistance with related topics such as number theory or practical applications of fractions and decimals, explore UpStudy’s live tutor question bank or our AI-powered problem-solving services today! Enhance your learning experience with UpStudy!