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. They are often used in everyday life, such as when cooking or measuring ingredients. A simplified fraction is a fraction that has been reduced to its lowest terms, meaning that the numerator and denominator have no common factors other than 1. In this article, we will explore which simplified fraction is equal to 0.17.

Understanding Decimals and Fractions

A decimal is a number that has a point as the separator between the whole number part and the fractional part. For example, 0.17 is a decimal that represents 17 hundredths. A fraction, on the other hand, is a way to represent a part of a whole using a numerator and a denominator. For example, 17/100 is a fraction that represents 17 hundredths.

Converting Decimals to Fractions

To convert a decimal to a fraction, we can use the following steps:

  1. Determine the place value of the last digit in the decimal. For example, if the last digit is in the hundredths place, the place value is 100.
  2. Write the decimal as a fraction by placing the decimal part over the place value. For example, 0.17 can be written as 17/100.
  3. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). For example, the GCD of 17 and 100 is 1, so the fraction 17/100 is already simplified.

Analyzing the Options

Now that we have converted 0.17 to a fraction, let's analyze the options:

A. {\frac{9}{17}$}∗∗B.∗∗** B. **{\frac{8}{45}\$} C. {\frac{17}{9}$}∗∗D.∗∗** D. **{\frac{16}{90}\$}

To determine which fraction is equal to 0.17, we can convert each option to a decimal and compare it to 0.17.

Converting Options to Decimals

Let's convert each option to a decimal:

A. {\frac{9}{17}$}$ To convert this fraction to a decimal, we can divide the numerator by the denominator: 9 ÷ 17 = 0.5294 (rounded to four decimal places).

B. {\frac{8}{45}$}$ To convert this fraction to a decimal, we can divide the numerator by the denominator: 8 ÷ 45 = 0.1778 (rounded to four decimal places).

C. {\frac{17}{9}$}$ To convert this fraction to a decimal, we can divide the numerator by the denominator: 17 ÷ 9 = 1.8889 (rounded to four decimal places).

D. {\frac{16}{90}$}$ To convert this fraction to a decimal, we can divide the numerator by the denominator: 16 ÷ 90 = 0.1778 (rounded to four decimal places).

Comparing Decimals

Now that we have converted each option to a decimal, let's compare them to 0.17:

  • Option A: 0.5294 (not equal to 0.17)
  • Option B: 0.1778 (equal to 0.17)
  • Option C: 1.8889 (not equal to 0.17)
  • Option D: 0.1778 (equal to 0.17)

Conclusion

Based on our analysis, we can conclude that options B and D are equal to 0.17. However, we need to check if these fractions are simplified.

Simplifying Fractions

Let's simplify options B and D:

B. {\frac{8}{45}$}$ The GCD of 8 and 45 is 1, so this fraction is already simplified.

D. {\frac{16}{90}$}$ We can simplify this fraction by dividing both the numerator and the denominator by their GCD, which is 2: 16 ÷ 2 = 8 and 90 ÷ 2 = 45. So, the simplified fraction is 8/45.

Final Answer

Based on our analysis, we can conclude that the simplified fraction equal to 0.17 is {\frac{8}{45}$}$.