https://r2.erweima.ai/mathbot/image/1726152334639ooe29bcl.jpg

The problem in the image is asking for the value of \( n \), given that:

\[
\frac{n}{270} = 0.1a48a48a48 \dots
\]

where the decimal repeats as \( 1a48 \) continuously, and \( n \) is a positive integer.

### Step 1: Express the repeating decimal
We represent the repeating decimal \( 0.1a48a48a48 \dots \) as a repeating fraction. Let:

\[
x = 0.1a48a48a48 \dots
\]

The repeating block is "1a48", so its length is 4 digits. We can express the repeating decimal as:

\[
x = 0.\overline{1a48}
\]

### Step 2: Convert repeating decimal to fraction
Let \( x = 0.\overline{1a48} \). Multiply \( x \) by 10000 to shift the decimal point over the repeating block:

\[
10000x = 1a48.1a48a48 \dots
\]

Now subtract the original \( x \) from this equation:

\[
10000x - x = 1a48.1a48a48 \dots - 0.1a48a48a48 \dots
\]

\[
9999x = 1a48
\]

Thus, we can express \( x \) as:

\[
x = \frac{1a48}{9999}
\]

### Step 3: Use the given fraction
From the problem, we know that:

\[
\frac{n}{270} = \frac{1a48}{9999}
\]

Multiplying both sides by 270 gives:

\[
n = \frac{1a48 \times 270}{9999}
\]

Now, we can solve for \( n \) once the value of \( a \) is known. If you provide any constraints on \( a \), we can find the exact value of \( n \).

Would you like more details, or do you have specific questions on how to proceed? 

Here are 5 questions to expand on this:

1. How do we calculate repeating decimals for other numbers?
2. Why does shifting the decimal point by multiplying help solve repeating decimals?
3. How can you convert more complex repeating decimals to fractions?
4. Can we solve similar problems involving different divisors or patterns?
5. What role does the length of the repeating block play in the solution?

**Tip**: Always express repeating decimals as fractions by multiplying them appropriately to eliminate the repeating part.

设n是一个正整数, 且 n/270 = 0.1a48a48a48...

Solve the repeating decimal problem where n is a positive integer and n/270 = 0.1a48a48.... Convert the repeating decimal to a fraction and solve for n. This problem is suitable for Grade 7 students and involves concepts of algebra and repeating decimals.

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