Fact-Checking Fraction Conversions: Why 4 and 3/4 Will Always Equal Exactly 4.75
Explore how Fact-Checking Fraction Conversions: Why 4 and 3/4 Will Always Equal Exactly 4.75 remains a key topic in this detailed write-up.
Q1: Is 4 and 3/4 a repeating or terminating decimal?
A1: It is strictly a terminating decimal. The decimal expansion stops cleanly at two digits after the decimal point (4.75) with zero remainder.
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Q2: How do you write 4 and 3/4 as an improper fraction?
A2: Multiply the whole number 4 by the denominator 4 (16), then add the numerator 3 to get 19. The improper fraction is 19/4.
Q3: What is 4 and 3/4 expressed as a percentage?
A3: It equals 475%. You calculate this by multiplying the decimal equivalent (4.75) by 100.
Q4: Why does the denominator 4 never produce a recurring decimal?
A4: In base-10 arithmetic, any fraction whose denominator's prime factorization contains only 2s or 5s terminates. Since 4 equals 2², it divides evenly into 100, leaving no infinite repeating cycle.
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