Converting a Fraction to a Decimal Number

Oct 13, 2025 by wbrum.org 33 views

Understanding the Problem

In this problem, we are given a fraction $$-1 \frac{7}{20}$ and asked to convert it into a decimal number. To solve this problem, we need to understand the concept of converting fractions to decimals and how to perform the necessary calculations.

What is a Decimal Number?

A decimal number is a number that is written in the form of a point (.) followed by digits. For example, 3.5, 2.75, and 0.25 are all decimal numbers. Decimal numbers can be used to represent fractions, and they can also be used to represent whole numbers.

Converting a Fraction to a Decimal Number

To convert a fraction to a decimal number, we need to divide the numerator (the top number) by the denominator (the bottom number). In this case, the numerator is 7 and the denominator is 20.

Performing the Division

To perform the division, we need to divide 7 by 20. This can be done using long division or a calculator.

Using Long Division

To use long division, we need to write the division problem in the following format:

  ____________________
20 | 7

We then need to divide 7 by 20. To do this, we can start by dividing 7 by 20, which gives us 0 with a remainder of 7. We can then multiply 20 by 0 and subtract the result from 7, which gives us 7. We can then bring down a 0 and divide 70 by 20, which gives us 3 with a remainder of 10. We can then multiply 20 by 3 and subtract the result from 70, which gives us 10. We can then bring down a 0 and divide 100 by 20, which gives us 5 with a remainder of 0. Therefore, the result of the division is 0.35.

Using a Calculator

To use a calculator, we can simply type in the division problem and press the "=" button. This will give us the result of the division, which is 0.35.

Converting the Mixed Number to a Decimal Number

Now that we have converted the fraction to a decimal number, we need to convert the mixed number to a decimal number. To do this, we need to add the whole number part to the decimal number part. In this case, the whole number part is -1 and the decimal number part is 0.35. Therefore, the result of the conversion is -1.35.

Conclusion

In this problem, we were given a fraction $$-1 \frac{7}{20}$ and asked to convert it into a decimal number. To solve this problem, we needed to understand the concept of converting fractions to decimals and how to perform the necessary calculations. We used long division and a calculator to convert the fraction to a decimal number, and then we added the whole number part to the decimal number part to get the final result.

Key Takeaways

To convert a fraction to a decimal number, we need to divide the numerator by the denominator.
We can use long division or a calculator to perform the division.
To convert a mixed number to a decimal number, we need to add the whole number part to the decimal number part.

Common Mistakes

Not understanding the concept of converting fractions to decimals.
Not performing the division correctly.
Not adding the whole number part to the decimal number part.

Real-World Applications

Converting fractions to decimals is an important skill that is used in many real-world applications, such as:

Cooking: When a recipe calls for a fraction of an ingredient, we need to convert it to a decimal number to measure it accurately.
Building: When building a structure, we need to convert fractions to decimals to measure the dimensions accurately.
Science: When conducting experiments, we need to convert fractions to decimals to measure the results accurately.

Conclusion

$In conclusion, converting a fraction to a decimal number is an important skill that is used in many real-world applications. By understanding the concept of converting fractions to decimals and how to perform the necessary calculations, we can solve problems and make accurate measurements.<br/> **Frequently Asked Questions (FAQs)**$

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

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal number is a way of expressing a number as a point (.) followed by digits.

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

A: To convert a fraction to a decimal number, you need to divide the numerator (the top number) by the denominator (the bottom number). You can use long division or a calculator to perform the division.

Q: What is the easiest way to convert a fraction to a decimal number?

A: The easiest way to convert a fraction to a decimal number is to use a calculator. Simply type in the fraction and press the "=" button to get the decimal equivalent.

Q: Can I convert a mixed number to a decimal number?

A: Yes, you can convert a mixed number to a decimal number by adding the whole number part to the decimal number part. For example, the mixed number 3 1/2 can be converted to a decimal number by adding 3 to 0.5, which gives 3.5.

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

A: To convert a decimal number to a fraction, you need to express the decimal number as a ratio of two numbers. For example, the decimal number 0.5 can be expressed as the fraction 1/2.

Q: What is the difference between a terminating decimal and a non-terminating decimal?

A: A terminating decimal is a decimal number that has a finite number of digits after the point (.), while a non-terminating decimal is a decimal number that has an infinite number of digits after the point (.).

Q: Can I convert a non-terminating decimal to a fraction?

A: Yes, you can convert a non-terminating decimal to a fraction by expressing the decimal number as a ratio of two numbers. For example, the non-terminating decimal 0.333... can be expressed as the fraction 1/3.

Q: How do I convert a fraction to a percentage?

A: To convert a fraction to a percentage, you need to divide the numerator (the top number) by the denominator (the bottom number) and then multiply the result by 100.

Q: Can I convert a percentage to a fraction?

A: Yes, you can convert a percentage to a fraction by dividing the percentage by 100 and then expressing the result as a ratio of two numbers.

Q: What is the difference between a simple fraction and a complex fraction?

A: A simple fraction is a fraction that has a single numerator and a single denominator, while a complex fraction is a fraction that has a fraction in the numerator or the denominator.

Q: Can I convert a complex fraction to a decimal number?

A: Yes, you can convert a complex fraction to a decimal number by simplifying the fraction and then converting it to a decimal number.

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

A: To convert a fraction to a decimal number with a negative sign, you need to follow the same steps as converting a positive fraction to a decimal number, but with a negative sign in front of the result.

Q: Can I convert a decimal number with a negative sign to a fraction?

A: Yes, you can convert a decimal number with a negative sign to a fraction by expressing the decimal number as a ratio of two numbers and then adding a negative sign in front of the result.

Conclusion

In conclusion, converting fractions to decimal numbers is an important skill that is used in many real-world applications. By understanding the concept of converting fractions to decimals and how to perform the necessary calculations, you can solve problems and make accurate measurements.