Clearing Decimals With Powers Of 10

Property To write decimals as integers, multiply the entire equation by a power of 10. Hint: Multiply by a power of 10 that will make the decimal with the most decimal places an integer, for example $0.008 \times 1000 = 8$.

Examples To solve $0.007x + 0.03 = 0.4$, multiply every term by 1000: $1000(0.007x) + 1000(0.03) = 1000(0.4)$, which simplifies to $7x + 30 = 400$. To solve $9 + 0.4x = 11.4$, multiply every term by 10: $10(9) + 10(0.4x) = 10(11.4)$, which simplifies to $90 + 4x = 114$.

Explanation Decimal points slowing you down? Just zap them! By multiplying every single term in an equation by a power of 10 (like 100 or 1000), you can magically turn all those tricky decimals into friendly whole numbers. This makes solving the equation much easier, so you can avoid messy decimal calculations and get to the answer faster.