What Is 1.75 As A Fraction

What is 1.75 as a Fraction? A Comprehensive Guide

Understanding how to convert decimals to fractions is a fundamental skill in mathematics. This comprehensive guide will delve into the process of converting the decimal 1.75 into a fraction, explaining the steps involved and providing further examples to solidify your understanding. We'll also explore some real-world applications and address common misconceptions.

Understanding Decimals and Fractions

Before we dive into the conversion, let's briefly review the concepts of decimals and fractions.

Decimals: Decimals represent numbers that are not whole numbers. They use a decimal point to separate the whole number part from the fractional part. The digits to the right of the decimal point represent tenths, hundredths, thousandths, and so on. For example, in the decimal 1.75, the '1' represents one whole unit, the '7' represents seven tenths (7/10), and the '5' represents five hundredths (5/100).

Fractions: Fractions represent parts of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). The numerator indicates how many parts you have, and the denominator indicates how many parts make up the whole. For example, in the fraction ¾, the numerator is 3 and the denominator is 4, meaning you have 3 out of 4 parts.

Converting 1.75 to a Fraction: Step-by-Step

The conversion of 1.75 to a fraction involves several simple steps:

Step 1: Write the decimal as a fraction with a denominator of 1.

This is the foundational step. We write 1.75 as a fraction: 1.75/1. This doesn't change the value, just its representation.

Step 2: Remove the decimal point by multiplying both the numerator and denominator by a power of 10.

Since 1.75 has two digits after the decimal point, we multiply both the numerator and denominator by 100 (10²):

(1.75 x 100) / (1 x 100) = 175/100

This step eliminates the decimal point, making the subsequent steps easier. It's crucial to remember that multiplying both the numerator and the denominator by the same number doesn't change the value of the fraction; it simply changes its representation.

Step 3: Simplify the fraction.

The fraction 175/100 is not in its simplest form. To simplify, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both 175 and 100 without leaving a remainder. In this case, the GCD is 25.

We divide both the numerator and the denominator by 25:

175 ÷ 25 = 7 100 ÷ 25 = 4

This simplifies the fraction to 7/4.

Step 4: Convert to a mixed number (optional).

The fraction 7/4 is an improper fraction (the numerator is larger than the denominator). We can convert it into a mixed number, which consists of a whole number and a proper fraction. To do this, we divide the numerator (7) by the denominator (4):

7 ÷ 4 = 1 with a remainder of 3

This means that 7/4 is equal to 1 and 3/4, or 1 ¾.

Therefore, 1.75 as a fraction is 7/4 or 1 ¾. Both representations are correct, and the choice between them depends on the context and the desired form.

Further Examples of Decimal to Fraction Conversion

Let's practice with a few more examples to reinforce the process:

Example 1: Converting 0.25 to a fraction

1. Write as a fraction: 0.25/1
2. Multiply by 100: (0.25 x 100) / (1 x 100) = 25/100
3. Simplify: 25/100 = 1/4

Therefore, 0.25 as a fraction is 1/4.

Example 2: Converting 2.3 to a fraction

1. Write as a fraction: 2.3/1
2. Multiply by 10: (2.3 x 10) / (1 x 10) = 23/10
3. This is already in its simplest form. It can also be expressed as a mixed number: 2 3/10

Therefore, 2.3 as a fraction is 23/10 or 2 3/10.

Example 3: Converting 0.625 to a fraction

1. Write as a fraction: 0.625/1
2. Multiply by 1000: (0.625 x 1000) / (1 x 1000) = 625/1000
3. Simplify (GCD is 125): 625/1000 = 5/8

Therefore, 0.625 as a fraction is 5/8.

Real-World Applications

Understanding decimal-to-fraction conversion is crucial in various real-world scenarios:

• Cooking and Baking: Recipes often use fractions (e.g., ½ cup, ¾ teaspoon). Being able to convert decimal measurements from digital scales to fractions ensures accuracy.
• Construction and Engineering: Precise measurements are essential. Converting decimal measurements to fractions allows for accurate calculations and material estimations.
• Finance: Calculating interest rates, discounts, and proportions often involves working with both decimals and fractions.
• Science: In scientific experiments and data analysis, converting between decimals and fractions might be necessary for specific calculations or representations.

Common Misconceptions

• Incorrect Simplification: Failing to simplify the fraction to its lowest terms is a common mistake. Always check if the numerator and denominator share any common factors.
• Forgetting the Whole Number: When converting a decimal larger than 1, remember to include the whole number part in your final answer (as in the mixed number form).
• Incorrect Multiplication: Ensure you multiply both the numerator and denominator by the correct power of 10 to eliminate the decimal point. Multiplying only the numerator will lead to an incorrect result.

Conclusion

Converting decimals to fractions is a valuable skill with wide-ranging applications. By following the steps outlined in this guide and practicing with various examples, you can master this fundamental mathematical concept. Remember to always simplify your fraction to its lowest terms and consider the context when deciding whether to express your answer as an improper fraction or a mixed number. This comprehensive understanding will undoubtedly enhance your mathematical abilities and problem-solving skills in numerous situations.