# Converting 4.6 to a Fraction: A Comprehensive Guide

Fractions are a fundamental concept in mathematics, representing parts of a whole. Converting decimals to fractions is a crucial skill for students and professionals alike. This article delves into the process of converting 4.6 to a fraction, providing a step-by-step guide and exploring the underlying principles.

### Key Facts

1. Write 4.6 as a fraction: 4.6/1.
2. Multiply both the numerator and denominator by 10 for each digit after the decimal point. In this case, there is one digit after the decimal point, so we multiply by 10: 4.6 x 10/1 x 10 = 46/10.
3. To simplify the fraction, find the Greatest Common Factor (GCF) of the numerator and denominator. The factors of 46 are 1, 2, 23, and 46, while the factors of 10 are 1, 2, 5, and 10. The GCF of 46 and 10 is 2.
4. Divide both the numerator and denominator by the GCF value: 46 ÷ 2/10 ÷ 2 = 23/5.

Therefore, 4.6 can be expressed as the fraction 23/5[3].

## Step 1: Writing 4.6 as a Fraction

To convert 4.6 to a fraction, we begin by writing it as a fraction with a denominator of 1: 4.6/1. This represents 4.6 as a whole number divided by 1.

## Step 2: Multiplying Numerator and Denominator

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point. In this case, there is one digit after the decimal point, so we multiply by 10: 4.6 x 10/1 x 10 = 46/10.

This step essentially shifts the decimal point to the right, converting the decimal into a whole number. Multiplying both the numerator and denominator by the same number ensures that the value of the fraction remains unchanged.

## Step 3: Simplifying the Fraction

To simplify the fraction 46/10, we find the Greatest Common Factor (GCF) of the numerator and denominator. The GCF is the largest number that divides both numbers without leaving a remainder.

The factors of 46 are 1, 2, 23, and 46, while the factors of 10 are 1, 2, 5, and 10. The GCF of 46 and 10 is 2.

Dividing both the numerator and denominator by the GCF simplifies the fraction: 46 ÷ 2/10 ÷ 2 = 23/5.

### Conclusion

Therefore, 4.6 can be expressed as the fraction 23/5. This conversion process involves writing the decimal as a fraction with a denominator of 1, multiplying both the numerator and denominator by 10 for each digit after the decimal point, and simplifying the fraction by finding the GCF of the numerator and denominator.

References

## FAQs

### What is the first step in converting 4.6 to a fraction?

Write 4.6 as a fraction with a denominator of 1: 4.6/1.

### How do I multiply the numerator and denominator to convert the decimal to a whole number?

Multiply both the numerator and denominator by 10 for each digit after the decimal point.

### What is the Greatest Common Factor (GCF) of 46 and 10?

The GCF of 46 and 10 is 2.

### How do I simplify the fraction 46/10?

Divide both the numerator and denominator by the GCF: 46 ÷ 2/10 ÷ 2 = 23/5.

23/5.

### Can I convert other decimals to fractions using the same process?

Yes, the same process can be used to convert any decimal to a fraction.

### What are some examples of other decimals that I can convert to fractions?

You can convert decimals like 0.25, 0.75, 1.33, 2.67, and so on to fractions using the same process.

### Why is it important to be able to convert decimals to fractions?

Converting decimals to fractions is a fundamental skill in mathematics, as it allows us to represent parts of a whole and perform various mathematical operations more easily.