Decimal to Ratio Calculator

How to Convert Decimals to Ratios

Converting decimals to ratios is a fundamental mathematical skill that's useful in various fields, from basic arithmetic to advanced sciences. Here's a comprehensive guide on how to perform this conversion:

Conversion Formula

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

1. Multiply the decimal by a power of 10 to eliminate the decimal point.
2. Express this as a fraction over the same power of 10.
3. Simplify the fraction if possible.

The general formula is:

\[ \text{Decimal} = \frac{\text{Decimal} \times 10^n}{10^n} \]

Where n is the number of decimal places in the original number.

Calculation Steps

Let's go through an example to convert 0.75 to a ratio:

Step 1: Identify the decimal places

0.75 has 2 decimal places.

Step 2: Convert decimal to a fraction

Multiply both the numerator and denominator by 10²:

\[ 0.75 = \frac{0.75 \times 10^2}{10^2} = \frac{75}{100} \]

Step 3: Simplify the fraction

Find the greatest common divisor (GCD) of 75 and 100:

\[ GCD(75, 100) = 25 \]

Divide both the numerator and denominator by the GCD:

\[ \frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \]

Step 4: Express as a ratio

The simplified fraction can be expressed as the ratio:

\[ 3:4 \]

Visual Representation

A visual representation can help understand the relationship between the decimal and its ratio form:

This diagram illustrates how 0.75 (or 3:4) relates to the whole (1). The blue portion represents 0.75 or 3/4 of the entire bar.