If (10000x = 0.5625), what is the value of (x)?
Answer and explanation
Correct answer: 0.00005625
The governing algebraic idea is to isolate the variable by performing the inverse operation on both sides. Since 10000 is multiplying x, divide both sides by 10000: x = 0.5625/10000. Dividing by 10,000 moves the decimal point four places to the left. Starting with 0.5625, the successive shifts give 0.05625, 0.005625, 0.0005625, and finally 0.00005625. Hence x = 0.00005625, so option C is correct. Option A ignores the division, option B shifts the decimal only three places, and option D shifts it only two places. Substitution confirms the result because 10,000 × 0.00005625 = 0.5625.
Frequently asked questions
What is the correct answer to this question?
0.00005625
Why is this the correct answer?
The governing algebraic idea is to isolate the variable by performing the inverse operation on both sides. Since 10000 is multiplying x, divide both sides by 10000: x = 0.5625/10000. Dividing by 10,000 moves the decimal point four places to the left. Starting with 0.5625, the successive shifts give 0.05625, 0.005625, 0.0005625, and finally 0.00005625. Hence x = 0.00005625, so option C is correct. Option A ignores the division, option B shifts the decimal only three places, and option D shifts it only two places. Substitution confirms the result because 10,000 × 0.00005625 = 0.5625.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.
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