To analyze which expression can be modeled using the number line described, let's first understand what the number line is representing.
The number line ranges from 0 to 1 and is divided into increments of \( \frac{1}{10} \). The arrows extend between these increments until \( \frac{7}{10} \). Essentially, this indicates that we are focusing on the segment of the number line that corresponds to \( \frac{7}{10} \) and dividing it into smaller parts of \( \frac{1}{10} \).
Next, let's break down the expressions:
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\( \frac{1}{10} \div 7 \): This expression represents dividing a small fraction (\( \frac{1}{10} \)) by a whole number (7). It does not correspond to our focus on \( \frac{7}{10} \).
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\( \frac{7}{10} \div \frac{1}{10} \): This expression represents how many \( \frac{1}{10} \) segments fit into \( \frac{7}{10} \). Since \( \frac{7}{10} \) contains 7 segments of \( \frac{1}{10} \), this would indeed be relevant for the number line up to \( \frac{7}{10} \).
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\( \frac{1}{10} \div \frac{7}{10} \): This expression represents how many \( \frac{7}{10} \)s can fit into \( \frac{1}{10} \). It does not reflect our focus on \( \frac{7}{10} \).
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\( 7 \div \frac{7}{10} \): This expression represents how many \( \frac{7}{10} \)s can fit into 7, which is also not directly relevant to the number line focusing on moving towards \( \frac{7}{10} \).
Out of these options, the expression that best models the scenario described on the number line moving to \( \frac{7}{10} \) is:
\( \frac{7}{10} \div \frac{1}{10} \).
So, the answer is:
\( \frac{7}{10} \div \frac{1}{10} \).