What are the definitions and examples of approximation error, significant digits, and terminating decimals?

a) The difference between exact and approximated value is called: The difference between an exact value and an approximated value is known as the approximation error. The correct option is ii). ii) approximation error b) Which one has 4 significant digits? To determine the number of significant digits: i) 0.0012: The leading zeros are not significant. The significant digits are 1 and 2. This has 2 significant digits. ii) 0.0125: The leading zeros are not significant. The significant digits are 1, 2, and 5. This has 3 significant digits. iii) 63.27: All non-zero digits are significant. The significant digits are 6, 3, 2, and 7. This has 4 significant digits. iv) 0.356: The leading zero is not significant. The significant digits are 3, 5, and 6. This has 3 significant digits. The correct option is iii). iii) 63.27 c) Which fraction shows the terminating decimal? A fraction represents a terminating decimal if, when simplified, the prime factors of its denominator are only 2s and 5s. i) (6)/(5): The denominator is 5. Since 5 is a prime factor, this is a terminating decimal (6 ÷ 5 = 1.2). ii) (7)/(13): The denominator is 13. Since 13 is not 2 or 5, this is a non-terminating, repeating decimal. iii) (5)/(3): The denominator is 3. Since 3 is not 2 or 5, this is a non-terminating, repeating decimal (5 ÷ 3 = 1.666...). iv) (5)/(9): The denominator is 9 = 3^2. Since 3 is not 2 or 5, this is a non-terminating, repeating decimal (5 ÷ 9 = 0.555...). The correct option is i). i) (6)/(5) d) The union of rational and irrational numbers is called: Rational numbers* are numbers that can be expressed as a fraction (p)/(q) where p and q are integers and q ≠ 0. Irrational numbers* are numbers that cannot be expressed as a simple fraction (e.g., sqrt(2), ). The set of all rational and irrational numbers together forms the set of real numbers. The correct option is iii). iii) real numbers Send me the next one 📸