1.26 as a fraction

2 min read 02-02-2025

1.26 as a Fraction: A Step-by-Step Guide

Title Tag: 1.26 as a Fraction: Simple Steps & Explanation

Meta Description: Learn how to convert the decimal 1.26 into a fraction. This easy-to-follow guide provides a step-by-step solution, explaining the process clearly and concisely. Master decimal-to-fraction conversions today!

Understanding Decimals and Fractions

Before we begin converting 1.26 to a fraction, let's quickly refresh our understanding of decimals and fractions. A decimal represents a part of a whole number, using a decimal point to separate the whole number from the fractional part. A fraction, on the other hand, represents a part of a whole number as a ratio of two integers (numerator and denominator).

Converting 1.26 to a Fraction: The Process

Converting 1.26 to a fraction involves these simple steps:

Write the decimal as a fraction over 1: This is our starting point. We write 1.26 as 1.26/1.
Multiply the numerator and denominator by 100: Since there are two digits after the decimal point (2 and 6), we multiply both the numerator and denominator by 100 (10 to the power of the number of decimal places). This moves the decimal point two places to the right. This gives us (1.26 x 100) / (1 x 100) = 126/100.
Simplify the fraction: Now, we need to simplify the fraction 126/100 by finding the greatest common divisor (GCD) of 126 and 100. The GCD of 126 and 100 is 2.
Divide both the numerator and denominator by the GCD: Dividing both the numerator and denominator by 2, we get (126 ÷ 2) / (100 ÷ 2) = 63/50.

Therefore, 1.26 as a fraction is 63/50.

Understanding the Result: 63/50

The fraction 63/50 is an improper fraction because the numerator (63) is larger than the denominator (50). This means it represents a value greater than 1. We can also express this as a mixed number:

Convert to a mixed number: To convert 63/50 to a mixed number, we divide 63 by 50. This gives us a quotient of 1 and a remainder of 13. Therefore, the mixed number representation is 1 13/50.

Both 63/50 and 1 13/50 are correct representations of 1.26 as a fraction. The best form to use depends on the context.

Practical Applications and Further Exploration

Converting decimals to fractions is a fundamental skill with applications across various fields, including:

Mathematics: Solving equations, simplifying expressions, and understanding rational numbers.
Science: Measuring quantities, recording experimental data, and performing calculations.
Engineering: Designing structures, calculating dimensions, and interpreting measurements.

This process can be applied to convert any decimal to a fraction. Remember to adjust the multiplier (10, 100, 1000, etc.) based on the number of decimal places in the original number. Practice with different decimals to build confidence and mastery of this essential mathematical skill.

Frequently Asked Questions (FAQs)

Q: Can I convert any decimal to a fraction?

A: Yes, you can convert any terminating decimal (a decimal that ends) to a fraction using this method. Repeating decimals (decimals with digits that repeat infinitely) require a slightly different approach.

Q: What if the fraction isn't easily simplified?

A: If the GCD is 1, then the fraction is already in its simplest form. Use a calculator or prime factorization to find the GCD if needed.

Q: Why is it important to simplify fractions?

A: Simplifying fractions makes them easier to work with and understand. It presents the fraction in its most concise and efficient form.