Convert the following terminating decimals as fractions
75.35

Answer

To convert the terminating decimal 75.35 into a fraction, we can follow these steps:

### Step 1: Write the decimal as a fraction
We start by writing the decimal number 75.35 as a fraction. Since there are two digits after the decimal point, we can express it as:

\[ 75.35 = \frac{7535}{100} \]

### Step 2: Simplify the fraction
Next, we need to simplify the fraction \(\frac{7535}{100}\). To do this, we will find the greatest common divisor (GCD) of the numerator (7535) and the denominator (100).

### Step 3: Find the GCD
We can find the GCD of 7535 and 100 by factoring both numbers or using the Euclidean algorithm. However, for simplicity, we can check for divisibility by common factors.

Both numbers can be divided by 5:

- \(7535 \div 5 = 1507\)
- \(100 \div 5 = 20\)

### Step 4: Write the simplified fraction
Now we can write the simplified fraction:

\[ \frac{7535}{100} = \frac{1507}{20} \]

### Final Answer
Thus, the terminating decimal 75.35 as a fraction is:

\[ \frac{1507}{20} \]