Decimal to Ratio Calculator

Convert decimal numbers to ratios and ratios to decimal numbers accurately with our free online calculator. Whether you need to find the ratio equivalent of a decimal or calculate the decimal value of a ratio, our tool handles all the math for you, including simplification to lowest terms.

Calculation Type:

Standard
Step by Step
Chart View

Result

Detailed Steps

Visual Representation

Formulas

Converting a Decimal to a Ratio

To convert a decimal to a ratio, we need to find the fraction form and simplify:

Decimal d = Fraction a/b = Ratio a:b

Converting a Ratio to a Decimal

To convert a ratio to a decimal, divide the first number by the second:

Ratio a:b = Decimal a÷b

Simplifying a Ratio

To simplify a ratio, divide both numbers by their greatest common divisor (GCD):

Simplified a:b = (a÷GCD):(b÷GCD)

How to Use the Decimal to Ratio Calculator

Decimal to Ratio Conversion

  1. Select the “Decimal to Ratio” option from the Calculation Type dropdown.
  2. Enter your decimal number (e.g., 0.75).
  3. Optionally, adjust the precision level (default is 5).
  4. Choose your preferred display mode (Standard, Step by Step, or Chart).
  5. Click the “Calculate” button.
  6. View your results in your chosen display format.

Ratio to Decimal Conversion

  1. Select the “Ratio to Decimal” option from the Calculation Type dropdown.
  2. Enter the first value of your ratio in the left input field.
  3. Enter the second value of your ratio in the right input field.
  4. Choose your preferred display mode (Standard, Step by Step, or Chart).
  5. Click the “Calculate” button.
  6. View your results in your chosen display format.

Frequently Asked Questions (FAQs)

What is a ratio?

A ratio is a mathematical expression that represents the relationship between two or more quantities. It compares values, showing how many times one value contains another. For example, the ratio 3:4 shows that the first quantity is 3/4 of the second quantity.

How do you convert a decimal to a ratio?

To convert a decimal to a ratio:

  1. Multiply the decimal by powers of 10 until you get a whole number (removing the decimal point)
  2. Use this whole number as the numerator
  3. Use the power of 10 as the denominator
  4. Simplify the resulting fraction by dividing both numbers by their greatest common divisor (GCD)

Can all decimals be expressed as ratios?

No, not all decimals can be expressed as ratios of whole numbers. Only rational numbers (terminating or repeating decimals) can be expressed as ratios. Irrational numbers like π (3.14159…) or √2 (1.41421…) cannot be expressed as exact ratios because they have non-repeating, non-terminating decimal expansions.

Ratios and fractions are closely related but used for different purposes. A ratio compares quantities and is typically written as a:b or a to b, while a fraction represents a part of a whole and is written as a/b. Every ratio a:b can be written as the fraction a/b, but fractions are not always thought of as ratios.

How accurate is this calculator?

This calculator is designed to handle most common decimal values and convert them to their exact ratio representation when possible. For repeating decimals, it uses an algorithm to detect the pattern and generate the accurate ratio. However, for extremely precise calculations or very complex repeating decimals, the precision setting can be adjusted to improve accuracy.