Express 2.0 15 Bar In The Form Of P By Q Where P And Q Are Integer And Q ≠ 0

Express 2.0 15 bar in the form of p by q where P and Q are integer and q ≠ 0

Understanding the Problem

Expressing a decimal number in the form of a fraction is a fundamental concept in mathematics. The given problem is to express 2.015 as a fraction in the form of p by q, where p and q are integers and q ≠ 0. This problem requires us to convert a decimal number into a fraction, which is a crucial skill in mathematics.

What is a Decimal Number?

A decimal number is a number that has a decimal point in it. It is a way of representing a number in a more precise and accurate manner. Decimal numbers can be expressed as fractions, which is a way of representing a number as the ratio of two integers.

Converting Decimal to Fraction

To convert a decimal number to a fraction, we need to follow a few simple steps. The first step is to identify the decimal number and determine the place value of the last digit. In this case, the decimal number is 2.015, and the last digit is 5, which is in the hundredths place.

Step 1: Identify the Decimal Number

The decimal number is 2.015.

Step 2: Determine the Place Value of the Last Digit

The last digit is 5, which is in the hundredths place.

Step 3: Multiply the Decimal Number by a Power of 10

To convert the decimal number to a fraction, we need to multiply it by a power of 10 that is equal to the place value of the last digit. In this case, we need to multiply 2.015 by 100, which is equal to the place value of the last digit.

2.015 × 100 = 201.5

Step 4: Subtract the Decimal Number from the Product

Now, we need to subtract the decimal number from the product. This will give us a whole number.

201.5 - 2.015 = 199.485

Step 5: Simplify the Result

The result is 199.485. We can simplify this by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Finding the GCD

To find the GCD, we need to list the factors of both numbers.

Factors of 199: 1, 199 Factors of 485: 1, 5, 97, 485

The greatest common divisor is 1.

Simplifying the Result

Since the GCD is 1, we cannot simplify the result further.

Expressing the Result as a Fraction

Now, we can express the result as a fraction.

199.485 = 199485/1000

Expressing the Result in the Form of p by q

We can express the result in the form of p by q by simplifying the fraction.

199485/1000 = 39897/200

Conclusion

In this article, we have learned how to express a decimal number in the form of a fraction. We have used the given decimal number 2.015 and converted it to a fraction in the form of p by q, where p and q are integers and q ≠ 0. The result is 39897/200.

Key Takeaways

• A decimal number can be expressed as a fraction.
• To convert a decimal number to a fraction, we need to multiply it by a power of 10 that is equal to the place value of the last digit.
• We need to subtract the decimal number from the product to get a whole number.
• We can simplify the result by dividing both the numerator and the denominator by their greatest common divisor (GCD).
• We can express the result in the form of p by q by simplifying the fraction.

Frequently Asked Questions

• Q: What is a decimal number? A: A decimal number is a number that has a decimal point in it.
• Q: How do I convert a decimal number to a fraction? A: To convert a decimal number to a fraction, you need to multiply it by a power of 10 that is equal to the place value of the last digit, subtract the decimal number from the product, and simplify the result.
• Q: What is the greatest common divisor (GCD)? A: The greatest common divisor (GCD) is the largest number that divides both numbers without leaving a remainder.

References

• [1] Khan Academy. (n.d.). Converting decimals to fractions. Retrieved from https://www.khanacademy.org/math/pre-algebra/pre-algebra-decimals/converting-decimals-to-fractions/v/converting-decimals-to-fractions
• [2] Math Open Reference. (n.d.). Converting decimals to fractions. Retrieved from https://www.mathopenref.com/convertingdecimals.html

Glossary

• Decimal number: A number that has a decimal point in it.
• Fraction: A way of representing a number as the ratio of two integers.
• Greatest common divisor (GCD): The largest number that divides both numbers without leaving a remainder.
• Place value: The position of a digit in a number.
• Power of 10: A number that is a power of 10, such as 10, 100, 1000, etc.
  Express 2.0 15 bar in the form of p by q where P and Q are integer and q ≠ 0: Q&A

Q: What is a decimal number?

A: A decimal number is a number that has a decimal point in it. It is a way of representing a number in a more precise and accurate manner.

Q: How do I convert a decimal number to a fraction?

A: To convert a decimal number to a fraction, you need to multiply it by a power of 10 that is equal to the place value of the last digit, subtract the decimal number from the product, and simplify the result.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both numbers without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, you need to list the factors of both numbers and find the largest number that is common to both lists.

Q: What is the place value of a digit?

A: The place value of a digit is the position of the digit in a number. For example, in the number 123.45, the place value of the digit 5 is hundredths.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD).

Q: What is the difference between a decimal number and a fraction?

A: A decimal number is a number that has a decimal point in it, while a fraction is a way of representing a number as the ratio of two integers.

Q: Can I express a decimal number in the form of p by q where p and q are integers and q ≠ 0?

A: Yes, you can express a decimal number in the form of p by q where p and q are integers and q ≠ 0. To do this, you need to convert the decimal number to a fraction and simplify the result.

Q: How do I express a decimal number in the form of p by q where p and q are integers and q ≠ 0?

A: To express a decimal number in the form of p by q where p and q are integers and q ≠ 0, you need to follow these steps:

1. Multiply the decimal number by a power of 10 that is equal to the place value of the last digit.
2. Subtract the decimal number from the product.
3. Simplify the result by dividing both the numerator and the denominator by their greatest common divisor (GCD).
4. Express the result in the form of p by q where p and q are integers and q ≠ 0.

Q: What is the result of expressing 2.015 in the form of p by q where p and q are integers and q ≠ 0?

A: The result of expressing 2.015 in the form of p by q where p and q are integers and q ≠ 0 is 39897/200.

Q: Can I use a calculator to express a decimal number in the form of p by q where p and q are integers and q ≠ 0?

A: Yes, you can use a calculator to express a decimal number in the form of p by q where p and q are integers and q ≠ 0. However, it is always a good idea to check your work by hand to make sure that the result is correct.

Q: What are some common mistakes to avoid when expressing a decimal number in the form of p by q where p and q are integers and q ≠ 0?

A: Some common mistakes to avoid when expressing a decimal number in the form of p by q where p and q are integers and q ≠ 0 include:

• Not multiplying the decimal number by a power of 10 that is equal to the place value of the last digit.
• Not subtracting the decimal number from the product.
• Not simplifying the result by dividing both the numerator and the denominator by their greatest common divisor (GCD).
• Not expressing the result in the form of p by q where p and q are integers and q ≠ 0.

Q: How do I check my work when expressing a decimal number in the form of p by q where p and q are integers and q ≠ 0?

A: To check your work when expressing a decimal number in the form of p by q where p and q are integers and q ≠ 0, you need to follow these steps:

1. Multiply the decimal number by a power of 10 that is equal to the place value of the last digit.
2. Subtract the decimal number from the product.
3. Simplify the result by dividing both the numerator and the denominator by their greatest common divisor (GCD).
4. Express the result in the form of p by q where p and q are integers and q ≠ 0.
5. Check that the result is correct by dividing the numerator by the denominator.

Q: What are some real-world applications of expressing a decimal number in the form of p by q where p and q are integers and q ≠ 0?

A: Some real-world applications of expressing a decimal number in the form of p by q where p and q are integers and q ≠ 0 include:

• Converting decimal numbers to fractions in mathematics and science.
• Expressing decimal numbers in the form of p by q where p and q are integers and q ≠ 0 in finance and economics.
• Using decimal numbers in the form of p by q where p and q are integers and q ≠ 0 in engineering and technology.

Q: Can I use a computer program to express a decimal number in the form of p by q where p and q are integers and q ≠ 0?

A: Yes, you can use a computer program to express a decimal number in the form of p by q where p and q are integers and q ≠ 0. However, it is always a good idea to check your work by hand to make sure that the result is correct.

Q: What are some common computer programs that can be used to express a decimal number in the form of p by q where p and q are integers and q ≠ 0?

A: Some common computer programs that can be used to express a decimal number in the form of p by q where p and q are integers and q ≠ 0 include:

• Microsoft Excel
• Google Sheets
• Python
• MATLAB

Q: Can I use a calculator to express a decimal number in the form of p by q where p and q are integers and q ≠ 0?

A: Yes, you can use a calculator to express a decimal number in the form of p by q where p and q are integers and q ≠ 0. However, it is always a good idea to check your work by hand to make sure that the result is correct.

Q: What are some common calculators that can be used to express a decimal number in the form of p by q where p and q are integers and q ≠ 0?

A: Some common calculators that can be used to express a decimal number in the form of p by q where p and q are integers and q ≠ 0 include:

• Texas Instruments TI-83
• Texas Instruments TI-84
• Casio FX-991EX
• HP 12C