*The decimal .175 can be expressed as the fraction 7/40. This fraction represents the same value as the decimal and is in its simplest form, making it easier to work with in mathematical calculations and applications.*

**Understanding Decimal Fractions:**

Decimal fractions are a fundamental concept in mathematics. They allow us to represent parts of a whole or quantities that are less than one. In this blog post, we will explore the decimal fraction .175 and delve into its significance, conversion, and application.

**What is .175 as a Fraction?**

To express .175 as a fraction, we first need to understand its decimal place value. In .175, the digit 1 is in the hundredths place (10^-2), the digit 7 is in the thousandths place (10^-3), and the digit 5 is in the ten-thousandths place (10^-4).

**Step 1: Convert the Decimal to a Fraction**

To convert .175 to a fraction, we can start by writing it as a fraction over a power of 10, based on its place value:

.175 = 175/1000

**Step 2: Simplify the Fraction**

Now, we can simplify the fraction 175/1000 by finding the greatest common divisor (GCD) of the numerator and denominator, which is 25:

175 ÷ 25 = 7 1000 ÷ 25 = 40

So, 175/1000 simplifies to 7/40.

**.175 as a Fraction:**

Therefore, .175 can be expressed as the fraction 7/40.

**Significance of .175:**

Understanding the fractional representation of decimals like .175 is crucial in various areas:

**Finance:**In financial calculations, interest rates, and percentage changes, decimal fractions play a significant role.**Engineering:**Engineers often work with measurements and calculations involving decimal fractions, ensuring precision in their designs and solutions.**Science:**In scientific research, precise measurements and data analysis may require dealing with decimal fractions.**Cooking and Baking:**Recipes often include measurements in decimal fractions, making it important for accurate cooking and baking.

**Converting Decimal Fractions:**

Converting decimals to fractions is a valuable skill. Knowing how to express decimal quantities as fractions can simplify calculations, comparisons, and conversions in various fields.

**Applications:**

**Math Education:**Teaching students how to convert decimals to fractions helps them grasp the concept of fractions and decimals.**Retail Pricing:**Pricing products and calculating discounts or sales tax may involve decimal fractions.**Medicine:**In healthcare, precise dosage calculations sometimes require working with decimal fractions.

**Conclusion:**

Decimal fractions, such as .175, are a fundamental aspect of mathematics and have practical applications in everyday life, from calculating prices to following recipes. Understanding how to convert decimals to fractions expands our mathematical toolkit and enhances our ability to work with numbers effectively. So, the next time you encounter a decimal like .175, remember that it can be expressed as the fraction 7/40, and this knowledge can be a valuable asset in various situations.

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