How do you convert the decimal 78.23 into a fraction?

To convert the decimal 78.23 into a fraction, we follow a systematic approach. Here’s a step-by-step guide:

1. Understand the Decimal: The decimal 78.23 consists of two parts: the whole number part (78) and the decimal part (0.23).
2. Convert the Whole Number: The whole number 78 can be represented as a fraction with a denomination of 1: 78 = ⁷⁸₁.
3. Convert the Decimal Part: To convert the decimal 0.23 into a fraction, we can identify it as a hundredth because there are two digits after the decimal point. Thus, 0.23 can be expressed as: 0.23 = ²³₁₀₀.
4. Combine the Fractions: Now we need to combine the whole number fraction ⁷⁸₁ and the fraction for the decimal part ²³₁₀₀. To do this, we can use a common denominator. The common denominator here would be 100. So, we rewrite the whole number as a fraction with the same denominator:
• 78 = ^{78 imes 100}_{1 imes 100} = ⁷⁸⁰⁰₁₀₀.
5. Add the Two Fractions: Now we can add the two fractions since they share the same denominator: ^{7800 + 23}₁₀₀ = ⁷⁸²³₁₀₀.
6. Final Result: Therefore, the decimal 78.23 as a fraction is: ⁷⁸²³₁₀₀.

For a complete fraction representation and to simplify it, we check for any common factors between 7823 and 100. Since 7823 is a prime number and does not share any factors with 100, this is the simplest form of the fraction.

In conclusion, the decimal 78.23 can be written as the fraction ⁷⁸²³₁₀₀.