Which Simplified Fraction Is Equal To 0.17?A. { \frac{9}{17}$}$ B. { \frac{8}{45}$}$ C. { \frac{17}{9}$}$ D. { \frac{16}{90}$}$

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Introduction

In mathematics, fractions are a way to represent a part of a whole. Simplifying fractions is an essential skill that helps us to express them in their simplest form. In this article, we will explore which simplified fraction is equal to 0.17.

Understanding Decimals and Fractions

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, 0.17 is a decimal number. On the other hand, a fraction is a way to represent a part of a whole using two numbers: a numerator (the top number) and a denominator (the bottom number). For example, 17/100 is a fraction.

Converting Decimals to Fractions

To convert a decimal to a fraction, we need to find the equivalent fraction. We can do this by dividing the decimal by 1 and then simplifying the result. Let's convert 0.17 to a fraction.

Step 1: Divide the Decimal by 1

0.17 ÷ 1 = 0.17

Step 2: Multiply the Decimal by a Power of 10

To make the decimal a whole number, we can multiply it by a power of 10. Let's multiply 0.17 by 100.

0.17 × 100 = 17

Step 3: Write the Result as a Fraction

Now that we have a whole number, we can write it as a fraction.

17/100

Simplifying the Fraction

The fraction 17/100 is not in its simplest form. We can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 17 and 100 is 1, so we cannot simplify the fraction further.

Comparing the Options

Now that we have the simplified fraction 17/100, let's compare it with the options given in the problem.

A. 917\frac{9}{17} B. 845\frac{8}{45} C. 179\frac{17}{9} D. 1690\frac{16}{90}

Option A: 917\frac{9}{17}

To compare option A with our simplified fraction, we need to find the equivalent fraction. We can do this by multiplying the numerator and the denominator by the same number. Let's multiply both the numerator and the denominator of option A by 100.

917×100100=9001700\frac{9}{17} \times \frac{100}{100} = \frac{900}{1700}

Now that we have the equivalent fraction, we can compare it with our simplified fraction. The two fractions are not equal.

Option B: 845\frac{8}{45}

To compare option B with our simplified fraction, we need to find the equivalent fraction. We can do this by multiplying the numerator and the denominator by the same number. Let's multiply both the numerator and the denominator of option B by 100.

845×100100=8004500\frac{8}{45} \times \frac{100}{100} = \frac{800}{4500}

Now that we have the equivalent fraction, we can compare it with our simplified fraction. The two fractions are not equal.

Option C: 179\frac{17}{9}

To compare option C with our simplified fraction, we need to find the equivalent fraction. We can do this by multiplying the numerator and the denominator by the same number. Let's multiply both the numerator and the denominator of option C by 100.

179×100100=1700900\frac{17}{9} \times \frac{100}{100} = \frac{1700}{900}

Now that we have the equivalent fraction, we can compare it with our simplified fraction. The two fractions are not equal.

Option D: 1690\frac{16}{90}

To compare option D with our simplified fraction, we need to find the equivalent fraction. We can do this by multiplying the numerator and the denominator by the same number. Let's multiply both the numerator and the denominator of option D by 100.

1690×100100=16009000\frac{16}{90} \times \frac{100}{100} = \frac{1600}{9000}

Now that we have the equivalent fraction, we can compare it with our simplified fraction. The two fractions are not equal.

Conclusion

In conclusion, the simplified fraction that is equal to 0.17 is 17100\frac{17}{100}. This fraction is not equal to any of the options given in the problem.

Final Answer

Q: What is a simplified fraction?

A: A simplified fraction is a fraction that has been reduced to its simplest form, where the numerator and denominator have no common factors other than 1.

Q: How do I simplify a fraction?

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

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

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

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

A: There are several ways to find the GCD of two numbers, including:

  • Listing the factors of each number and finding the greatest common factor
  • Using the Euclidean algorithm
  • Using a calculator or online tool

Q: What is the difference between a simplified fraction and a reduced fraction?

A: A simplified fraction is a fraction that has been reduced to its simplest form, where the numerator and denominator have no common factors other than 1. A reduced fraction is a fraction that has been reduced to its simplest form, but may still have a common factor other than 1.

Q: Can a fraction be both simplified and reduced?

A: Yes, a fraction can be both simplified and reduced. In fact, all simplified fractions are also reduced fractions.

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

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

  1. Multiply the decimal by a power of 10 to make it a whole number
  2. Write the result as a fraction
  3. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor

Q: What is the relationship between decimals and fractions?

A: Decimals and fractions are two ways of representing the same value. A decimal is a way of representing a number using a point (.) as a separator between the whole number part and the fractional part, while a fraction is a way of representing a part of a whole using two numbers: a numerator (the top number) and a denominator (the bottom number).

Q: Can a decimal be equal to a simplified fraction?

A: Yes, a decimal can be equal to a simplified fraction. In fact, all decimals can be represented as simplified fractions.

Q: How do I compare two fractions?

A: To compare two fractions, you can follow these steps:

  1. Find the least common multiple (LCM) of the two denominators
  2. Multiply both fractions by the LCM
  3. Compare the resulting fractions

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.

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

A: There are several ways to find the LCM of two numbers, including:

  • Listing the multiples of each number and finding the smallest common multiple
  • Using the prime factorization method
  • Using a calculator or online tool

Q: Can a fraction be equal to another fraction?

A: Yes, a fraction can be equal to another fraction. In fact, all fractions can be compared and equalized.

Q: How do I add or subtract fractions?

A: To add or subtract fractions, you need to follow these steps:

  1. Find the least common multiple (LCM) of the two denominators
  2. Multiply both fractions by the LCM
  3. Add or subtract the resulting fractions

Q: What is the relationship between fractions and percentages?

A: Fractions and percentages are two ways of representing the same value. A fraction is a way of representing a part of a whole using two numbers: a numerator (the top number) and a denominator (the bottom number), while a percentage is a way of representing a part of a whole using a number between 0 and 100.

Q: Can a fraction be equal to a percentage?

A: Yes, a fraction can be equal to a percentage. In fact, all fractions can be converted to percentages and vice versa.

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

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

  1. Divide the numerator by the denominator
  2. Multiply the result by 100

Q: What is the relationship between fractions and ratios?

A: Fractions and ratios are two ways of representing the same value. A fraction is a way of representing a part of a whole using two numbers: a numerator (the top number) and a denominator (the bottom number), while a ratio is a way of representing a comparison between two numbers.

Q: Can a fraction be equal to a ratio?

A: Yes, a fraction can be equal to a ratio. In fact, all fractions can be converted to ratios and vice versa.

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

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

  1. Write the fraction as a ratio
  2. Simplify the ratio by dividing both numbers by their greatest common divisor

Q: What is the relationship between fractions and proportions?

A: Fractions and proportions are two ways of representing the same value. A fraction is a way of representing a part of a whole using two numbers: a numerator (the top number) and a denominator (the bottom number), while a proportion is a way of representing a comparison between two ratios.

Q: Can a fraction be equal to a proportion?

A: Yes, a fraction can be equal to a proportion. In fact, all fractions can be converted to proportions and vice versa.

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

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

  1. Write the fraction as a ratio
  2. Write the ratio as a proportion
  3. Simplify the proportion by dividing both numbers by their greatest common divisor