Understanding Decimal Powers
Powers with decimal bases work just like whole number powers, but with an extra decimal twist!
When you see something like (0.5)² or (1.2)³, it means you multiply the decimal by itself the number of times shown by the exponent. The tricky part is keeping track of the decimal places, but we'll show you how to make it easy!
How to Calculate Decimal Powers
1️⃣ Write it out - Show the multiplication (e.g., 0.4³ = 0.4 × 0.4 × 0.4)
2️⃣ Multiply step by step - Multiply two numbers at a time
3️⃣ Count decimal places - The answer should have as many decimal places as all the numbers you multiplied together
Let's Practice Together!
Example 1: Calculate (0.5)²
First, let's write it out: 0.5 × 0.5
Now multiply 5 × 5 = 25
Count the decimal places: 0.5 has 1 decimal place, and we have two of them, so total of 2 decimal places
Place the decimal point: 0.25
Solution: (0.5)² = 0.5 × 0.5 = 0.25
Great job! Notice how the answer is smaller than the original number when we square a decimal between 0 and 1.
Example 2: Calculate (1.2)³
First step: 1.2 × 1.2 = ?
Try calculating this first step yourself!
12 × 12 = 144
Now count decimal places: 1.2 has 1 decimal place, and we have two of them, so total of 2 decimal places
1.2 × 1.2 = 1.44
Now multiply that result by 1.2 again: 1.44 × 1.2 = ?
144 × 12 = 1728
Count decimal places: 1.44 has 2, 1.2 has 1, total of 3 decimal places
Final answer: (1.2)³ = 1.728
Awesome! Notice how the answer gets bigger when we raise a number greater than 1 to a power.
Parent Tips 🌟
- Money makes it real: Use coins to demonstrate decimal powers. For example, show that 0.25 (a quarter) is 0.5 squared.
- Calculator check: Let your child work problems manually first, then verify with a calculator to build confidence.
- Growth visualization: Compare how numbers greater than 1 grow faster with exponents, while decimals between 0 and 1 get smaller.