Which fraction is equal to −1.125 on the number line?
Answer and explanation
Correct answer: −9/8
The governing concept is equivalence between a terminating decimal and a rational fraction, while preserving the sign. Write −1.125 as −1125/1000 because there are three decimal places. The greatest common divisor of 1125 and 1000 is 125, so divide numerator and denominator by 125: 1125 ÷ 125 = 9 and 1000 ÷ 125 = 8. Hence −1.125 = −9/8, making option A correct. Option B is the reciprocal of the positive magnitude and has value about −0.889. Option C loses the negative sign, placing the point to the right of zero, and option D equals −0.44, not −1.125. The negative sign must remain with the fraction throughout simplification.
Frequently asked questions
What is the correct answer to this question?
−9/8
Why is this the correct answer?
The governing concept is equivalence between a terminating decimal and a rational fraction, while preserving the sign. Write −1.125 as −1125/1000 because there are three decimal places. The greatest common divisor of 1125 and 1000 is 125, so divide numerator and denominator by 125: 1125 ÷ 125 = 9 and 1000 ÷ 125 = 8. Hence −1.125 = −9/8, making option A correct. Option B is the reciprocal of the positive magnitude and has value about −0.889. Option C loses the negative sign, placing the point to the right of zero, and option D equals −0.44, not −1.125. The negative sign must remain with the fraction throughout simplification.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers.
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