Step-by-Step Solution for Converting 1.78 to a Fraction

Step 1: Understand the Number

The number 1.78 is a decimal, which can be broken into two parts:

• The whole number part is: 1.
• The decimal part is: 0.78.

We aim to convert the entire number into a fraction.

Step 2: Isolate the Decimal Part (0.78)

Focus on the decimal part (0.78) and represent it as a fraction.

Step 2.1: Write 0.78 as \( \frac78100 \)

The decimal 0.78 can be read as "78 hundredths." Mathematically, this is:

\[ 0.78 = \frac78100 \]

Step 2.2: Simplify the Fraction

Now simplify \( \frac78100 \) by finding the greatest common divisor (GCD) of 78 and 100.

• The GCD of 78 and 100 is: 2.
• Therefore, the simplified fraction is:

\[ \frac3950 \]

Step 3: Combine the Whole Number and Fraction

The original number 1.78 is the sum of the whole number 1 and the fraction \( \frac3950 \).

Combine these as a mixed number:

\[ 1.78 = 1 + \frac3950 = \frac89/50 \]

Step 4: Verify the Answer

To verify, divide \( \frac89/50 \):

\[ \frac89/50 = 1.78 \]

Thus, the fraction is correct.

Final Answer

The decimal 1.78 as a fraction is:

\[ \frac89/50 \]

If expressed as a mixed number:

\[ 1 39/50 \]