Yes, ratios can absolutely have decimals. A ratio is simply a comparison between two quantities, and there is no mathematical rule requiring those quantities to be whole numbers. You’ll encounter decimal ratios regularly in currency exchange rates, financial analysis, science, and everyday problem-solving.
Why Decimals in Ratios Are Valid
A ratio compares two quantities, and those quantities can be whole numbers, fractions, or decimals. The BBC Bitesize math curriculum notes that “ratios are usually written using integers, but not always,” and gives currency exchange as a common example: the exchange rate of pounds to euros might be written as 1 : 1.19. That’s a perfectly valid ratio with a decimal on one side.
Ratios can also be expressed as a single decimal value by dividing the first term by the second. A ratio of 20 : 80 equals 0.25 in decimal form. A ratio of 4 : 5 equals 0.8. This is just division, and the result doesn’t need to come out to a neat whole number.
Where You’ll See Decimal Ratios
In finance, decimal ratios are the norm. A company’s current ratio (which measures its ability to pay short-term debts) is typically expressed as a single decimal number, like 1.3 or 0.9. Nobody converts these to whole numbers because the decimal form is more precise and more useful.
The golden ratio, famous in art and nature, is the irrational number 1.6180339… with decimals that never end and never repeat. It cannot be written as a ratio of two whole numbers, which is exactly what makes it irrational, yet it’s still called a ratio.
In chemistry, decimal ratios appear constantly during empirical formula calculations. When chemists determine the composition of a compound, they divide mole quantities to find ratios like 1.2 : 2.4 : 1. Those decimal ratios are then multiplied by a common factor (in this case, 5) to reach whole numbers for the final chemical formula. The decimal ratio is a necessary step in the process.
How to Simplify a Decimal Ratio to Whole Numbers
While decimal ratios are valid, many textbooks and problems ask you to simplify them into whole numbers. The process is straightforward:
- Multiply all parts by a power of 10 to eliminate the decimals. If you have one decimal place, multiply by 10. Two decimal places, multiply by 100. Choose the smallest power of 10 that makes every term a whole number.
- Find the highest common factor of the resulting whole numbers and divide each term by it.
For example, a ratio of 1.5 : 6 : 2.8 becomes 15 : 60 : 28 after multiplying everything by 10. The highest common factor of 15, 60, and 28 is 1, so that ratio is already in simplest whole-number form. If you had 1.5 : 6 : 2.4 instead, multiplying by 10 gives 15 : 60 : 24. The highest common factor of those three numbers is 3, so dividing each by 3 gives the simplified ratio 5 : 20 : 8.
Decimals vs. Whole Numbers: When Each Form Works Best
Whole-number ratios are easier to visualize. Saying “for every 5 red marbles there are 3 blue ones” is more intuitive than saying “the ratio of red to blue is 1.67.” That’s why most introductory math classes emphasize simplifying ratios to whole numbers. Students first encounter ratios in grade 6, where the focus is on connecting ratios to whole-number multiplication and division. By grade 7, the curriculum introduces ratios involving fractions and decimals, including unit rates like “2 miles per hour” derived from dividing 1/2 mile by 1/4 hour.
Decimal ratios shine when precision matters or when one side of the ratio is fixed at 1. A financial analyst saying “the debt-to-equity ratio is 0.75” communicates instantly that debt is three-quarters the size of equity. Converting that to 3 : 4 is equivalent, but less conventional in that field. Similarly, saying “there are 0.5 apples for every orange” works perfectly well when you’re describing an average across a large quantity.
Sometimes the decimal form is unavoidable. Repeating decimals like 0.333… (from a 1 : 3 ratio) are messier to work with than the fraction 1/3, which is one reason fractions and whole-number ratios remain useful. But the decimal version isn’t wrong. It’s just a different way of expressing the same relationship.
The Short Answer
Ratios can contain decimals on either side (like 1 : 1.19), be expressed as a single decimal value (like 0.75), or even be irrational decimals that never terminate (like 1.618…). The form you use depends on context. If a problem asks for a simplified ratio, convert to whole numbers. If you’re working in finance, science, or any field where precision matters, decimal ratios are standard.