To divide \( 8.464 \) by \( 0.04 \), we can follow these steps:
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Convert the divisor to a whole number: Since \( 0.04 \) is not a whole number, we can multiply both the numerator (the dividend) and the denominator (the divisor) by \( 100 \) to eliminate the decimal in the divisor.
\[ 8.464 \div 0.04 = \frac{8.464 \times 100}{0.04 \times 100} = \frac{846.4}{4} \]
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Divide the numbers: Now, we divide \( 846.4 \) by \( 4 \).
To perform the division:
- \( 4 \) goes into \( 8 \) two times (since \( 4 \times 2 = 8 \)).
- Subtract \( 8 \) from \( 8 \) to get \( 0 \); bring down the next digit \( 4 \).
- \( 4 \) goes into \( 4 \) one time (since \( 4 \times 1 = 4 \)).
- Subtract \( 4 \) from \( 4 \) to get \( 0 \); bring down the next digit \( 6 \).
- \( 4 \) goes into \( 6 \) one time (since \( 4 \times 1 = 4 \)).
- Subtract \( 4 \) from \( 6 \) to get \( 2 \); bring down the next digit \( 0 \) (from the decimal).
- \( 4 \) goes into \( 20 \) five times (since \( 4 \times 5 = 20 \)).
- Subtract \( 20 \) from \( 20 \) to get \( 0 \).
Putting it all together, we have:
\[ 846.4 \div 4 = 211.6 \]
- Final Answer: Thus,
\[ 8.464 \div 0.04 = 211.6 \]
So, the final answer is
\[ \boxed{211.6} \]