Is 1/3 greater than 0.3? Are they equal? Explain your reasoning.

Question

Is 1/3 greater than 0.3? Are they equal? Explain your reasoning.

Answer 1

1/3 > 0.3

convert them both to decimal form and compare them

1/3 = 0.333...

0.3 = 0.3000...

0.333...> 0.300...

so 1/3 > 0.3

1/3 = 0.3 + 0.0333...

or convert them to fractions with the same denominator, and compare the numerators

0.3 = 3/10

0.3 ==3(3)/10(3) = 9/30 multiply numerator and denominator by the same number and its an equivalent fraction. 3/3 = 1. 3/10 times 1 = 3/10. (3/3)(3/10) = 9/30 = 3/10

1/3 = 10(1)/10(3) = 10/30

10/30 > 9/30

because 10>9, 10 30ths > 9 30ths, 10/30<9/30, just as 10 apples is greater than 9 apples

so 1/3 > 0.3