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The value of (0.1×0.001×0.0001×106) is:
1
101
100
1001
1001
Count the total number of decimal places in the factors. (1 + 3 + 4) = 8 decimal places. The term 10⁶ has 6 zeros. Total result = 10⁻⁸ * 10⁶ = 10⁻² = 0.01 = 1/100.
Expression to evaluate: (0.1 × 0.001 × 0.0001 × 10⁶)
10a×10b=10a+b
Count the total number of decimal places in the factors. (1 + 3 + 4) = 8 decimal places. The term 10⁶ has 6 zeros. Total result = 10⁻⁸ * 10⁶ = 10⁻² = 0.01 = 1/100.
Confusing the number of zeros in 0.0001 (which is 4 decimal places) or miscalculating the exponent addition (10⁻¹ * 10⁻³ * 10⁻⁴ = 10⁻⁸).
Convert decimals to powers of 10
Express each decimal number as a power of 10: 0.1=10−1, 0.001=10−3, 0.0001=10−4, and the final term is 106.
10−1×10−3×10−4×106
Apply exponent rules
Sum the exponents of 10: −1+(−3)+(−4)+6=−8+6=−2.
10−1−3−4+6=10−2
Simplify the final result
Calculate 10−2, which is equivalent to 1001.
10−2=1001
D is correct because the product evaluates to 10−2, which is equal to 1001.
This concept of manipulating powers of 10 is fundamental for solving physics numericals involving unit conversions like micro (10⁻⁶) to milli (10⁻³) or standard SI units.
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