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The correct expression of 8.46 in the fractional form is ________.
99838тАЛ
9983тАЛ
99846тАЛ
9984тАЛ
99838тАЛ
To convert a number with a repeating decimal part (where the whole part is 'I' and the repeating part 'R' has 'n' digits), write the whole part plus the repeating digits over as many 9s as there are repeating digits.
The repeating decimal is 8.46 where 46 repeats infinitely.
x=I+99RтАЛ
To convert a number with a repeating decimal part (where the whole part is 'I' and the repeating part 'R' has 'n' digits), write the whole part plus the repeating digits over as many 9s as there are repeating digits.
Students often write it as 846/99 or 846/100, forgetting that the 8 is the whole number part and the 46 is the repeating part.
Define the number
Let the number be x=8.46. This can be split into the integer part and the repeating fraction part: x=8+0.46.
x=8+0.46
Convert the repeating part
The repeating decimal 0.46 has two repeating digits. Thus, it is represented by the fraction 9946тАЛ.
0.46=9946тАЛ
Combine to find the final fraction
Add the integer part 8 to the fraction 9946тАЛ: x=8+9946тАЛ=998├Ч99+46тАЛ.
x=99792+46тАЛ=99838тАЛ
A is correct because the repeating decimal 8.46 simplifies to the fraction 99838тАЛ.
This concept is essential for simplifying complex expressions in arithmetic and is frequently tested in 'Number System' modules.
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