Introduction:
In mathematics, decimals are a way of representing fractions or rational numbers. A decimal is a number that includes a decimal point, separating the whole number part from the fractional part. Every decimal can be written as a fraction, which is a ratio of two integers. This is true for any decimal, whether it is a terminating decimal or a repeating decimal.

Explanation:
To understand why every decimal can be written as a fraction, let's break it down into steps:

Step 1: Understanding decimals and place value:
Decimals are based on the decimal system, which uses powers of 10. Each digit in a decimal has a specific place value, such as units, tenths, hundredths, etc. For example, in the decimal 3.14, the digit 3 represents 3 units, the digit 1 represents 1 tenth, and the digit 4 represents 4 hundredths.

Step 2: Converting decimals to fractions:
To convert a decimal to a fraction, we need to understand the place value of each digit. The digit to the right of the decimal point represents the tenths place, the next digit represents the hundredths place, and so on.

Step 3: Writing the decimal as a fraction:
To write a decimal as a fraction, we use the place value of each digit. The numerator of the fraction is the decimal number without the decimal point, and the denominator is based on the place value of the last digit. For example, the decimal 0.5 can be written as the fraction 5/10, which can be simplified to 1/2.

Step 4: Simplifying the fraction:
Once the decimal is written as a fraction, we can simplify it if possible. In the example above, the fraction 1/2 can be simplified to its lowest terms, which is also the simplest form of the fraction.

Conclusion:
In conclusion, every decimal can be written as a fraction. By understanding the place value of each digit in the decimal and converting it to a fraction, we can represent any decimal as a ratio of two integers. This concept is fundamental in mathematics and helps us work with decimals more easily.

That's why because
for example:
4.3=43\10