Solving Decimal Equations

You may find it easier to solve an equation with integers instead of decimals. One way to solve an equation that includes decimals is to first multiply each side of the equation by the same power of ten to get an equivalent equation that has integer coefficients instead of decimal coefficients.

When you do this, be sure to multiply each side of the equation by the power of ten that will eliminate all decimals. For example, multiply by 100 if there are decimals in the hundredths place, multiply by 1000 if there are decimals in the thousandths place, and so on. And be sure that you multiply each side of the equation by the same power of ten, or you will not get an equation that is equivalent to the original.

If you are comfortable using decimals, you can solve equations which include decimals without multiplying each side of the equation by a power of ten to eliminate decimal coefficients.

Method for Solving Equations in One Variable

• Step1: Simplify both sides by removing group symbols and collect like terms.
• Step2: Remove fractions (or decimals) by multiplying both sides by a suitable factor (L.C.M. of fractions or a power of 10 in case.
  • Multiply each term on both sides of the equation by 10, 100, 1,000, etc. to get whole numbers. In some situations you may have to simplify the equation before multiplying on both sides.
  • Every term in the equation must be multiplied by the same number.
  • Follow the same steps for solving equations
  • If the directions ask you to round the answer but it come out a fraction, do the division and perform rounding.

Eliminate decimals by multiplying both sides of the equation by a power of 10 that will make the entire coefficients integer. Get the variable terms on one side. Get the constant terms on one side. Isolate the variable