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The value of (0.04 × 0.04 × 0.04) is equal to:
0.000064
0.0064
0.00064
0.064
0.000064
Count the number of decimal places in each factor (2 + 2 + 2 = 6). The final answer must have exactly 6 digits after the decimal point.
We are given the decimal multiplication of 0.04 repeated three times.
(a×10−n)3=a3×10−3n
Count the number of decimal places in each factor (2 + 2 + 2 = 6). The final answer must have exactly 6 digits after the decimal point.
Students often count only 4 decimal places instead of 6, incorrectly selecting 0.0064 instead of 0.000064.
Convert decimals to scientific notation
Express 0.04 as a product of an integer and a power of ten: 0.04=4×10−2.
0.04=4×10−2
Apply the cube power
Substitute this into the expression (4×10−2)3 and apply the power rule for exponents: (a⋅b)n=an⋅bn.
(4×10−2)3=43×(10−2)3=64×10−6
Convert back to decimal notation
The expression 64×10−6 indicates that the decimal point must be moved 6 places to the left, which results in 0.000064.
64×10−6=0.000064
A is correct because the product of 0.04×0.04×0.04 results in 0.000064.
This digit counting technique is essentially the same as used in calculating significant figures in Physics or handling large powers in Compound Interest problems.