Change The Fraction $\frac{7}{12}$ To A Decimal. Round Your Answer To The Nearest Thousandth.A) 1.700 B) 0.583 C) 0.600 D) 1.714

Feb 26, 2025 by ADMIN 132 views

**Converting Fractions to Decimals: A Step-by-Step Guide**

Introduction

In mathematics, fractions and decimals are two ways to represent the same value. A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal is a way of expressing a number in a base-10 system. In this article, we will focus on converting fractions to decimals and provide a step-by-step guide on how to do it.

What is a Fraction?

A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of two parts: the numerator (the top number) and the denominator (the bottom number). For example, the fraction $\frac{7}{12}$ represents 7 parts out of 12 equal parts.

Converting Fractions to Decimals

To convert a fraction to a decimal, we need to divide the numerator by the denominator. In the case of the fraction $\frac{7}{12}$ , we need to divide 7 by 12.

Step 1: Divide the Numerator by the Denominator

To divide 7 by 12, we can use long division or a calculator. Using long division, we get:

  0.583
12 | 7.000
  -6.000
  ------
    1.000
  -0.900
  ------
    0.100
  -0.090
  ------
    0.010

Step 2: Round the Answer to the Nearest Thousandth

Once we have the decimal equivalent of the fraction, we need to round it to the nearest thousandth. In this case, we need to round 0.583 to the nearest thousandth.

Rounding Rules

To round a number to the nearest thousandth, we need to look at the digit in the ten-thousandths place. If it is 5 or greater, we round up. If it is less than 5, we round down.

In this case, the digit in the ten-thousandths place is 0, which is less than 5. Therefore, we round down to 0.583.

Conclusion

In conclusion, converting fractions to decimals is a simple process that involves dividing the numerator by the denominator and rounding the answer to the nearest thousandth. By following the steps outlined in this article, you can easily convert fractions to decimals and solve problems that involve fractions and decimals.

Answer

The correct answer is B) 0.583.

Discussion

This problem is a great example of how fractions and decimals are related. By converting the fraction $\frac{7}{12}$ to a decimal, we can see that it is equal to 0.583. This is a useful skill to have in mathematics, as it allows us to work with fractions and decimals in a more intuitive way.

Real-World Applications

Converting fractions to decimals has many real-world applications. For example, in cooking, we often need to convert fractions to decimals in order to measure ingredients accurately. In science, we often need to convert fractions to decimals in order to calculate quantities such as density and pressure.

Practice Problems

Here are a few practice problems to help you practice converting fractions to decimals:

Convert the fraction $\frac{3}{8}$ to a decimal.
Convert the fraction $\frac{9}{16}$ to a decimal.
Convert the fraction $\frac{5}{12}$ to a decimal.

Answer Key

0.375
0.5625
0.4167

Conclusion

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

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal is a way of expressing a number in a base-10 system.

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

A: To convert a fraction to a decimal, you need to divide the numerator by the denominator. For example, to convert the fraction $\frac{7}{12}$ to a decimal, you would divide 7 by 12.

Q: What if the denominator is not a whole number?

A: If the denominator is not a whole number, you can still convert the fraction to a decimal by dividing the numerator by the denominator. For example, to convert the fraction $\frac{3}{4}$ to a decimal, you would divide 3 by 4.

Q: How do I round a decimal to the nearest thousandth?

A: To round a decimal to the nearest thousandth, you need to look at the digit in the ten-thousandths place. If it is 5 or greater, you round up. If it is less than 5, you round down.

Q: What if I get a repeating decimal?

A: If you get a repeating decimal, you can still convert the fraction to a decimal by dividing the numerator by the denominator. For example, to convert the fraction $\frac{1}{3}$ to a decimal, you would get 0.333... (where the dots represent the repeating decimal).

Q: Can I use a calculator to convert fractions to decimals?

A: Yes, you can use a calculator to convert fractions to decimals. Simply enter the fraction in the calculator and it will give you the decimal equivalent.

Q: Are there any shortcuts for converting fractions to decimals?

A: Yes, there are several shortcuts for converting fractions to decimals. For example, you can use the fact that $\frac{1}{2}$ is equal to 0.5, $\frac{1}{4}$ is equal to 0.25, and $\frac{1}{8}$ is equal to 0.125.

Q: Can I convert a decimal to a fraction?

A: Yes, you can convert a decimal to a fraction by dividing the decimal by 1 and then simplifying the result. For example, to convert the decimal 0.5 to a fraction, you would divide 0.5 by 1 and get $\frac{1}{2}$ .

Q: Are there any real-world applications for converting fractions to decimals?

A: Yes, there are many real-world applications for converting fractions to decimals. For example, in cooking, you may need to convert fractions to decimals in order to measure ingredients accurately. In science, you may need to convert fractions to decimals in order to calculate quantities such as density and pressure.

Q: Can I use a spreadsheet to convert fractions to decimals?

A: Yes, you can use a spreadsheet to convert fractions to decimals. Simply enter the fraction in the spreadsheet and it will give you the decimal equivalent.

Q: Are there any online tools for converting fractions to decimals?

A: Yes, there are many online tools for converting fractions to decimals. For example, you can use a calculator or a spreadsheet online to convert fractions to decimals.