To divide 8.464 by 0.04, we can follow these steps:
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Convert the divisor (0.04) into a whole number by multiplying both the numerator (8.464) and the divisor (0.04) by 100 (which shifts the decimal point two places to the right).
\[ 8.464 \div 0.04 = \frac{8.464 \times 100}{0.04 \times 100} = \frac{846.4}{4} \]
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Now divide 846.4 by 4.
To do this step by step:
- First, consider how many times 4 fits into 84 (the first two digits of 846.4).
- 4 goes into 8 two times (2 x 4 = 8). Subtract 8 from 8 to get 0. Bring down the next digit (4) to make 04.
- 4 fits into 4 one time (1 x 4 = 4). Subtract 4 from 4 to get 0. Bring down the next digit (6) to make 06.
- 4 goes into 6 one time (1 x 4 = 4). Subtract 4 from 6 to get 2. Bring down the decimal and a zero (to consider the 2).
- Now consider how many times 4 fits into 20. 4 goes into 20 five times (5 x 4 = 20). Subtract 20 from 20 to get 0.
Putting this together:
- 84 divided by 4 gives 21,
- 06 divided by 4 gives 1,
- And the decimal gives us an additional digit divided to form 5.
- First, consider how many times 4 fits into 84 (the first two digits of 846.4).
Thus, \[ 846.4 \div 4 = 211.6 \]
So, \[ 8.464 \div 0.04 = 211.6 \]
Thus, the final answer is:
\[ \boxed{211.6} \]