How to solve equations with decimals
An equation with decimals works the same way as one with integers, but we can make the arithmetic easier before we solve. We’ll pick a power of 10 that clears every decimal and multiply both sides by it.
Choose the power of 10 using place value
Find the decimal that goes farthest to the right. If it ends in the tenths place, multiply both sides by . If it ends in the hundredths place, multiply by . For thousandths, use . Multiplying both sides by the same nonzero number keeps the equation equivalent, and the distributive property applies that multiplier to each term.
Example: Clear a decimal in the tenths place
In , the only decimal goes to the tenths place. Multiply both sides by .
Check in the original equation: .
Example: Clear a negative decimal
In , multiplying both sides by clears the decimal on the right. The right side stays negative.
Example: Clear decimals with different place values
In , the left side goes to the tenths place and the right side goes to the hundredths place. Multiplying by turns all three numbers into integers.
To check, substitute for . The left side gives , which matches the right side.
