**.625 as a fraction**

Decimal numbers are a common way to represent parts of a whole, but they can sometimes feel abstract and difficult to understand. Fractions, on the other hand, offer a more concrete way to visualize and manipulate parts of a whole. In this guide, we will explore how to express the decimal number **.625 as a fraction**, providing a detailed explanation of the steps involved and offering helpful examples for better understanding.

## Understanding Decimals and Fractions

Decimals: A decimal is a number written with a decimal point (.) separating the whole number part from the fractional part. To the right of the decimal point, each digit represents a specific power of 10.

**For example, in the number 0.625 as a fraction**:

- 6 represents six tenth
- 2 represents two hundredth
- 5 represents five thousandth

**Fractions**: A fraction represents a part of a whole. It is written as two numbers separated by a horizontal line, where the top number (numerator) represents the number of parts taken, and the bottom number (denominator) represents the total number of parts. For example, the fraction 5/8 represents five out of eight parts.

## Converting Decimals to Fractions

**There are two main methods for converting a decimal to a fraction.**

**1. Place Value Method**:

This method involves analyzing the decimal value based on the place value of each digit.

- Write down the decimal without the decimal point.
- Count the number of digits to the right of the last non-zero digit. This number represents the denominator of the fraction, and its value will be 10 raised to that power.
- Write each digit of the decimal as the numerator, assigning the appropriate place value.
- Simplify the fraction if possible by finding the greatest common factor (GCD) of the numerator and denominator.

**Example: Convert .625 to a fraction.**

- Write the decimal without the decimal point: 625
- Count the digits to the right of the last non-zero digit: 3
- Denominator: 10^3 = 1000
- Numerator: 625
- Fraction: 625/1000
- Simplify: 625/1000 = ⅝

### 2. Multiplication and Division Method:

This method involves multiplying both the numerator and the denominator by a suitable power of 10 to move the decimal point to the desired position.

- Choose a power of 10 that will move the decimal point to the end of the number (without creating trailing zeros).
- Multiply both the numerator and denominator by that power of 10.
- The decimal will now be converted into a whole number, which represents the numerator of the fraction.
- The denominator remains the same as the chosen power of 10.

**Example: Convert .625 to a fraction.**

- Choose a power of 10: 1000 (moves the decimal point 3 positions to the right)
- Multiply both numerator and denominator: 625 * 1000 = 625000
- Denominator: 1000
- Fraction: 625000/1000 = 625/10 = 5/8

## Conclusion

Converting a decimal to a fraction requires understanding the place value system and applying simple mathematical operations. Both the place value method and the multiplication and division method offer effective approaches to achieving this conversion. By following the steps outlined in this guide and practicing with different examples, you can confidently express decimal numbers as fractions and vice versa.