Convert 0.77 to a rational number in simplest form.

Question

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. 🌟