The rational number representation of -0.0675 is:
(A) [tex]-\frac{5}{8}[/tex]
(B) [tex]-\frac{13}{20}[/tex]
(C) [tex]-\frac{3}{5}[/tex]
(D) 4
The integer closest to [tex]\frac{59}{20}[/tex] is:
1
2
3
4
Answer (2)
To solve this problem, we need to determine the rational number representation of -0.0675 and find the integer closest to 20 59 .
Part 1: Rational Number Representation of -0.0675
A rational number can be expressed as a fraction b a , where a and b are integers and b = 0 .
To convert -0.0675 to a rational number:
Write the decimal as a fraction:
-0.0675 can be expressed as − 10000 675 because there are four digits after the decimal point.
Simplify the fraction:
First, find the greatest common divisor (GCD) of 675 and 10000, which is 25.
Divide both the numerator and the denominator by their GCD: − 10000 ÷ 25 675 ÷ 25 = − 400 27
The simplified rational number is − 400 27 . None of the given multiple-choice options directly match this, so it's possible that a mistake was made in the options listed.
Part 2: Integer Closest to 20 59
To find the closest integer to 20 59 :
Calculate the decimal value:
Divide 59 by 20: 20 59 = 2.95 .
Round to the nearest integer:
Since 2.95 is closer to 3 than 2, the integer closest to 20 59 is 3.
Chosen Option: 3 for the integer closest to 20 59 .
In conclusion, the closest integer is 3.
The rational number representation of -0.0675 is − 400 27 , which does not match the provided options. The integer closest to 20 59 is 3. Hence, the chosen option is 3 for that question.
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