Write $\frac{75}{16}$ As A Decimal.

Feb 26, 2025 by ADMIN 38 views

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

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Introduction

In mathematics, converting fractions to decimals is an essential skill that is used in various applications, including finance, science, and engineering. A fraction is a way of expressing a part of a whole, while a decimal is a way of expressing a number in a base-10 system. In this article, we will focus on converting the fraction $\frac{75}{16}$ to a decimal.

Understanding Fractions and Decimals

A fraction is a way of expressing a part of a whole. It consists of two parts: the numerator (the top number) and the denominator (the bottom number). The numerator represents the number of equal parts, while the denominator represents the total number of parts. For example, the fraction $\frac{1}{2}$ represents one half of a whole.

A decimal, on the other hand, is a way of expressing a number in a base-10 system. It consists of a decimal point and one or more digits that follow it. The digits after the decimal point represent the fractional part of the number.

Converting Fractions to Decimals

To convert a fraction to a decimal, we need to divide the numerator by the denominator. This can be done using long division or a calculator.

Long Division Method

Long division is a method of dividing one number by another. It involves dividing the numerator by the denominator and finding the remainder. The remainder is then used to find the next digit of the decimal.

To convert the fraction $\frac{75}{16}$ to a decimal using long division, we can follow these steps:

Divide 75 by 16.
Find the remainder.
Bring down the next digit (if any).
Repeat steps 1-3 until the remainder is zero.

Using long division, we get:

  ____________________
16 | 75.000000000000
  - 64.000000000000
  ____________________
  11.000000000000
  -  8.000000000000
  ____________________
   3.000000000000
  -  2.000000000000
  ____________________
   1.000000000000
  -  0.000000000000
  ____________________
   1.000000000000

The result of the long division is 4.6875.

Calculator Method

Using a calculator, we can also convert the fraction $\frac{75}{16}$ to a decimal. To do this, we simply divide the numerator by the denominator.

Using a calculator, we get:

75 ÷ 16 = 4.6875

Conclusion

In this article, we have learned how to convert the fraction $\frac{75}{16}$ to a decimal using long division and a calculator. We have also discussed the importance of converting fractions to decimals in various applications.

Key Takeaways:

Converting fractions to decimals is an essential skill in mathematics.
Long division and calculators can be used to convert fractions to decimals.
The result of converting a fraction to a decimal is a decimal number.

Practice Problems:

Convert the fraction $\frac{25}{8}$ to a decimal.
Convert the fraction $\frac{9}{4}$ to a decimal.
Convert the fraction $\frac{7}{3}$ to a decimal.

References:

"Mathematics for Dummies" by Mark Ryan
"Algebra and Trigonometry" by Michael Sullivan
"Mathematics: A Very Short Introduction" by Timothy Gowers

Further Reading:

"Converting Fractions to Decimals: A Step-by-Step Guide" by Math Is Fun
"Fractions and Decimals: A Guide to Converting Between Them" by Khan Academy
"Converting Fractions to Decimals: A Tutorial" by Purplemath

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Introduction

In our previous article, we discussed how to convert fractions to decimals using long division and calculators. In this article, we will provide a Q&A guide to help you understand the concept of converting fractions to decimals.

Q&A

Q: What is a fraction?

A: A fraction is a way of expressing a part of a whole. It consists of two parts: the numerator (the top number) and the denominator (the bottom number).

Q: What is a decimal?

A: A decimal is a way of expressing a number in a base-10 system. It consists of a decimal point and one or more digits that follow it.

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

A: To convert a fraction to a decimal, you can use long division or a calculator. Long division involves dividing the numerator by the denominator and finding the remainder. The remainder is then used to find the next digit of the decimal. A calculator can also be used to convert a fraction to a decimal by simply dividing the numerator by the denominator.

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

A: A fraction is a way of expressing a part of a whole, while a decimal is a way of expressing a number in a base-10 system. Fractions are often used in mathematics and science, while decimals are often used in finance and engineering.

Q: Can I convert a decimal to a fraction?

A: Yes, you can convert a decimal to a fraction by using a calculator or by using long division. To convert a decimal to a fraction, you can use the following steps:

Determine the number of decimal places.
Multiply the decimal by a power of 10 to eliminate the decimal places.
Convert the resulting number to a fraction.

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

A: To convert a mixed number to a decimal, you can use the following steps:

Convert the whole number part to a decimal by dividing it by 1.
Convert the fraction part to a decimal by dividing the numerator by the denominator.
Add the decimal parts together.

Q: Can I convert a fraction to a decimal with a calculator?

A: Yes, you can convert a fraction to a decimal using a calculator. Simply divide the numerator by the denominator to get the decimal equivalent.

Q: What are some common fractions that can be converted to decimals?

A: Some common fractions that can be converted to decimals include:

$\frac{1}{2}$ = 0.5
$\frac{1}{4}$ = 0.25
$\frac{3}{4}$ = 0.75
$\frac{1}{3}$ = 0.333...
$\frac{2}{3}$ = 0.666...