When dividing a decimal by 100, you can use expanded form to understand how the digits shift.
We start with the expression:
\[ (3 \times _) + (4 \times 100) \]
We can replace the underscore with the appropriate decimal place value for clarity. For example, if we interpret the "3" as being in the tenths place (3.4), we express it in expanded form.
So, if we take \(4\) as a whole number and \(3\) as a decimal quantity, we can express \(3.4\) as:
\[ (3 \times 0.1) + (4 \times 1) = 0.3 + 4 \]
Then, we proceed to divide this sum by 100:
\[ (0.3 + 4) \div 100 \]
Now we calculate this:
\[ \frac{0.3 + 4}{100} = \frac{4.3}{100} \]
This means we move the decimal point two places to the left because we are dividing by 100:
So,
\[ 4.3 \div 100 = 0.043 \]
In summary, dividing \(4.3\) by \(100\) puts the decimal two places left, resulting in \(0.043\). Thus, the expression is:
\[ (3 \times 0.1) + (4 \times 1) \div 100 \rightarrow \frac{0.3 + 4}{100} = 0.043 \]
The digits shifted two places to the left because they are worth 100 times less than what they were before.
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