Clearing Decimals Using Powers of 10
Clearing Decimals Using Powers of 10 is a Grade 8 math technique from Reveal Math, Course 3, Module 3: Solve Equations with Variables on Each Side. When an equation contains decimal coefficients, multiplying both sides by a power of 10 (10, 100, 1000, etc.) eliminates the decimals and creates an equivalent equation with integer coefficients that is much easier to solve. The key is identifying the term with the most decimal places to determine which power of 10 to use. For example, if the greatest number of decimal places is two, multiply every term by 100. This skill is essential in 8th grade algebra because it simplifies solving multi-step equations and prevents decimal arithmetic errors.
Key Concepts
To clear decimals from an equation, multiply both sides by $10^n$, where $n$ is the greatest number of decimal places in any single term.
$$10^n(\text{Left Side}) = 10^n(\text{Right Side})$$.
Common Questions
How do you clear decimals from an equation?
Multiply both sides of the equation by a power of 10 equal to 10 raised to the number of decimal places in the term with the most decimal digits. For example, if the greatest number of decimal places is 2, multiply everything by 100.
Why would you clear decimals in an equation?
Clearing decimals converts decimal coefficients into integers, making the equation simpler to solve and reducing the chance of arithmetic errors. The resulting equation is equivalent to the original but much easier to work with.
What power of 10 should you use to clear decimals?
Identify the term with the greatest number of decimal places. Use 10 raised to that number: if the most decimal places is 1, multiply by 10; if 2, multiply by 100; if 3, multiply by 1000.
Does clearing decimals change the solution to an equation?
No. Multiplying both sides of an equation by the same nonzero number preserves equality. The resulting equation has the same solution as the original—you are applying the Multiplication Property of Equality.
When do students learn to clear decimals in equations?
In Grade 8 Reveal Math Course 3, clearing decimals is taught in Module 3: Solve Equations with Variables on Each Side, as a strategy for solving multi-step linear equations.
What is an example of clearing decimals in an equation?
To solve 0.05m - 0.2 = 1.15, the greatest number of decimal places is 2. Multiply every term by 100: 5m - 20 = 115. Now solve the simpler integer equation.