Question

Convert 0.77 to a rational number in simplest form.
Remember to show your work. And when you show your work, please break it down so easy that a 1st grader could understand it.

Answer 1

Sure! Let's turn the number **0.77** into a fraction (which is a type of rational number).

### Step 1: Understanding Decimal Places
The number **0.77** has two digits after the decimal point. This means that we can think of it in terms of hundredths (like 77 out of 100).

### Step 2: Write as a Fraction
We can write **0.77** as:
\[
\frac{77}{100}
\]

### Step 3: Simplifying the Fraction
Now, we want to see if this fraction can be simplified. Simplifying means making the numbers smaller while still keeping the same value.

#### Finding the Greatest Common Divisor (GCD)
We need to find a number that can divide both **77** and **100** evenly. This number is called the GCD.

- The factors of **77** are: 1, 7, 11, and 77.
- The factors of **100** are: 1, 2, 4, 5, 10, 20, 25, 50, and 100.

The largest number that is in both lists is **1**. This means **77** and **100** have no common factors besides **1**.

### Step 4: Final Fraction
Since we can't simplify further, the fraction **\(\frac{77}{100}\)** is already in its simplest form.

### Step 5: Conclusion
So, the rational number for **0.77** in simplest form is:
\[
\frac{77}{100}
\]

And that's it! 0.77 is the same as 77 out of 100 when we use a fraction.

Answer 2

Please simplify your work.

Answer 3

Sure! Let’s simplify the explanation to make it even easier.

### Step 1: Change 0.77 to a Fraction
- **0.77** means **77** out of **100**.
- We can write it as:
\[
\frac{77}{100}
\]

### Step 2: Simplify the Fraction
- We check if **77** and **100** can be divided by the same number.
- The biggest number they can both be divided by is **1**.
- So, we can't make the fraction smaller.

### Final Answer
- The simplest form of **0.77** is:
\[
\frac{77}{100}
\]

That's how we convert **0.77** to a fraction!

Answer 4

Make it even easier please and thank you.🤎

Answer 5

Of course! Let’s make it super simple.

### Step 1: Change 0.77 into a Fraction
- **0.77** can be written as **77 over 100**:
\[
\frac{77}{100}
\]

### Step 2: Check if it can be Simplified
- We look for the biggest number they can both be divided by.
- The only number is **1**.

### Final Answer
- So, the fraction **\(\frac{77}{100}\)** is already as simple as it gets!

That’s it! **0.77** is the same as **77/100**. 🌟