Express The Following Decimals In The Form $\frac{q}{5}$ Or As A Ratio Of Two Numbers.i) 0.6ii) 0.36iii) 1.27

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Introduction

In mathematics, decimals and fractions are two fundamental ways to represent numbers. While decimals are often used in everyday calculations, fractions provide a more precise and elegant way to express numbers. In this article, we will explore how to express decimals in the form $\frac{q}{5}$ or as a ratio of two numbers.

Expressing 0.6 as a Fraction

To express 0.6 as a fraction, we can use the following steps:

  • Multiply 0.6 by 10 to get 6.
  • Express 6 as a fraction: 6 = 6/1.
  • Since we multiplied by 10, we need to divide by 10 to get the correct fraction: 6/1 ÷ 10 = 6/10.
  • Simplify the fraction: 6/10 = 3/5.

Therefore, 0.6 can be expressed as the fraction 3/5.

Expressing 0.36 as a Fraction

To express 0.36 as a fraction, we can use the following steps:

  • Multiply 0.36 by 100 to get 36.
  • Express 36 as a fraction: 36 = 36/1.
  • Since we multiplied by 100, we need to divide by 100 to get the correct fraction: 36/1 ÷ 100 = 36/100.
  • Simplify the fraction: 36/100 = 9/25.

Therefore, 0.36 can be expressed as the fraction 9/25.

Expressing 1.27 as a Fraction

To express 1.27 as a fraction, we can use the following steps:

  • Multiply 1.27 by 100 to get 127.
  • Express 127 as a fraction: 127 = 127/1.
  • Since we multiplied by 100, we need to divide by 100 to get the correct fraction: 127/1 ÷ 100 = 127/100.
  • Simplify the fraction: 127/100 = 127/100.

However, we can further simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, 1.27 can be expressed as the fraction 127/100.

Conclusion

In conclusion, expressing decimals as fractions is a useful skill in mathematics. By following the steps outlined in this article, we can convert decimals to fractions in the form $\frac{q}{5}$ or as a ratio of two numbers. This skill is essential in various mathematical applications, including algebra, geometry, and calculus.

Real-World Applications

Expressing decimals as fractions has numerous real-world applications. For example:

  • In finance, fractions are used to represent interest rates and investment returns.
  • In science, fractions are used to represent measurements and ratios of physical quantities.
  • In engineering, fractions are used to represent dimensions and proportions of structures and machines.

Tips and Tricks

Here are some tips and tricks to help you express decimals as fractions:

  • Use the concept of place value to convert decimals to fractions.
  • Multiply the decimal by a power of 10 to get rid of the decimal point.
  • Express the resulting number as a fraction and simplify it.
  • Use the greatest common divisor to simplify the fraction.

Common Mistakes

Here are some common mistakes to avoid when expressing decimals as fractions:

  • Not multiplying the decimal by a power of 10 to get rid of the decimal point.
  • Not expressing the resulting number as a fraction.
  • Not simplifying the fraction.
  • Not using the greatest common divisor to simplify the fraction.

Conclusion

Introduction

In our previous article, we explored how to express decimals as fractions in the form $\frac{q}{5}$ or as a ratio of two numbers. In this article, we will answer some frequently asked questions about expressing decimals as fractions.

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

A: A decimal is a way to represent a number using a point (.) as a separator between the whole number part and the fractional part. For example, 0.5 is a decimal. A fraction, on the other hand, is a way to represent a number as a ratio of two integers. For example, 1/2 is a fraction.

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

A: To convert a decimal to a fraction, you can follow these steps:

  1. Multiply the decimal by a power of 10 to get rid of the decimal point.
  2. Express the resulting number as a fraction.
  3. Simplify the fraction.

For example, to convert 0.5 to a fraction, you can multiply it by 10 to get 5, then express it as a fraction: 5/1. Simplify the fraction to get 5/1.

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

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 without leaving a remainder.

Q: How do I simplify a fraction?

A: To simplify a fraction, you can follow these steps:

  1. Find the greatest common divisor (GCD) of the numerator and the denominator.
  2. Divide both the numerator and the denominator by the GCD.

For example, to simplify the fraction 12/18, you can find the GCD of 12 and 18, which is 6. Then, divide both the numerator and the denominator by 6 to get 2/3.

Q: Can I express a decimal as a fraction with a denominator other than 5?

A: Yes, you can express a decimal as a fraction with a denominator other than 5. To do this, you can follow the same steps as before, but multiply the decimal by a power of 10 that is a multiple of the desired denominator.

For example, to express 0.25 as a fraction with a denominator of 4, you can multiply it by 4 to get 1, then express it as a fraction: 1/4.

Q: What are some common mistakes to avoid when expressing decimals as fractions?

A: Here are some common mistakes to avoid when expressing decimals as fractions:

  • Not multiplying the decimal by a power of 10 to get rid of the decimal point.
  • Not expressing the resulting number as a fraction.
  • Not simplifying the fraction.
  • Not using the greatest common divisor to simplify the fraction.

Q: How do I know if a decimal can be expressed as a fraction?

A: Any decimal can be expressed as a fraction. However, some decimals may not have a finite decimal representation, such as 0.999... (where the dots represent an infinite number of 9s). In such cases, the decimal can be expressed as a fraction, but the fraction may have an infinite number of terms.

Conclusion

In conclusion, expressing decimals as fractions is a fundamental skill in mathematics. By following the steps outlined in this article and avoiding common mistakes, you can convert decimals to fractions in the form $\frac{q}{5}$ or as a ratio of two numbers. This skill is essential in various mathematical applications and has numerous real-world applications.