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Evaluate: 0.0672 div 0.21...

Evaluate:
`0.0672 div 0.21`

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To evaluate \( 0.0672 \div 0.21 \), we will follow these steps: ### Step 1: Remove the Decimal Points To make the division easier, we can eliminate the decimal points by multiplying both numbers by 1000 (the least common multiple of the denominators). This gives us: \[ 0.0672 \div 0.21 = \frac{0.0672 \times 1000}{0.21 \times 1000} = \frac{67.2}{21} \] ### Step 2: Perform the Division Now, we will divide \( 67.2 \) by \( 21 \). To do this, we can set it up as a long division. 1. **Divide 67 by 21**: - \( 21 \times 3 = 63 \) (this is the largest multiple of 21 that is less than 67) - Subtract \( 63 \) from \( 67 \): \[ 67 - 63 = 4 \] - Bring down the next digit (which is 2), making it \( 42 \). 2. **Divide 42 by 21**: - \( 21 \times 2 = 42 \) - Subtract \( 42 \) from \( 42 \): \[ 42 - 42 = 0 \] So, \( 67.2 \div 21 = 3.2 \). ### Step 3: Adjust for the Decimal Places Now, we need to consider the decimal places we removed initially. In \( 0.0672 \), there are 4 decimal places, and in \( 0.21 \), there are 2 decimal places. Therefore, the total number of decimal places we need to account for in our answer is \( 4 - 2 = 2 \). So, we place the decimal point in \( 3.2 \) two places from the right: \[ 3.2 \rightarrow 0.32 \] ### Final Answer Thus, the result of \( 0.0672 \div 0.21 \) is: \[ \boxed{0.32} \]
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