Equation with Decimals Calculator
Solve linear equations containing decimals with step-by-step solutions
Solving Equations with Decimals
Equations with decimals can be solved in two ways: working with decimals directly or clearing them first by multiplying by a power of 10.
Clearing Decimals Method
- Find the decimal with the most decimal places
- Multiply both sides by 10, 100, 1000, etc. to clear all decimals
- Solve the resulting equation with whole numbers
Example
Solve: 0.5x + 1.25 = 3.75
Max decimal places: 2 (from 1.25 and 3.75)
Multiply by 100:
50x + 125 = 375
Solve: 50x = 250
x = 5
Frequently Asked Questions
Should I clear decimals or work with them?
Clearing decimals is generally easier and less error-prone. Multiplying by a power of 10 converts everything to whole numbers, making calculations simpler.
How do I know which power of 10 to use?
Count the maximum number of decimal places in any number. Use 10 for 1 decimal place, 100 for 2, 1000 for 3, and so on.
What if decimals have different numbers of places?
Use the power of 10 that clears the decimal with the most places. This will automatically clear all decimals with fewer places too.
Can I convert decimals to fractions instead?
Yes, but it's usually more work. Converting 0.5 to 1/2 is simple, but 0.37 becomes 37/100, which may be harder to work with than just multiplying by 100.
Do I multiply every term?
Yes, multiply EVERY term on both sides by the same power of 10. Missing even one term will give you the wrong answer.
What about repeating decimals?
Repeating decimals like 0.333... are best converted to fractions (1/3) before solving, as they can't be cleared with a simple power of 10.