Convert the following decimals into fractions .
9.645

Answer

To convert the decimal 9.645 into a fraction, follow these steps:

### Step-by-Step Solution:

1. **Identify the Decimal**: The given decimal is 9.645.

2. **Count the Decimal Places**: Count how many digits are after the decimal point. In this case, there are 3 digits (6, 4, and 5).

3. **Write as a Fraction**: To convert the decimal to a fraction, write the decimal number as the numerator and use a power of 10 as the denominator. Since there are 3 digits after the decimal, the denominator will be 1000 (which is 10 raised to the power of 3).
\[ 9.645 = \frac{9645}{1000} \]

4. **Simplify the Fraction**: Now, we simplify the fraction \(\frac{9645}{1000}\). To do this, we need to find the greatest common divisor (GCD) of 9645 and 1000.

5. **Finding the GCD**: The GCD of 9645 and 1000 can be found by factoring both numbers or using the Euclidean algorithm. In this case, we can see that both numbers can be divided by 5.

- Dividing 9645 by 5 gives us 1929.
- Dividing 1000 by 5 gives us 200.

Thus, we can simplify:
\[ \frac{9645 \div 5}{1000 \div 5} = \frac{1929}{200} \]

6. **Final Fraction**: The simplified fraction for the decimal 9.645 is:
\[ \frac{1929}{200} \]

### Summary:
The decimal 9.645 can be expressed as the fraction \(\frac{1929}{200}\).

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