How to Multiply a Decimal by a Power of 10
Understanding how to multiply a decimal by a power of 10 is a fundamental skill in mathematics, especially when dealing with scientific notation, finance, and other real-world applications. Multiplying a decimal by a power of 10 can be a straightforward process if you follow the right steps. In this article, we will explore the method to multiply a decimal by a power of 10, and provide you with some practical examples to illustrate the concept.
Step 1: Identify the Power of 10
The first step in multiplying a decimal by a power of 10 is to identify the power of 10. A power of 10 is simply 10 raised to a certain exponent. For example, 10^2 represents 10 raised to the power of 2, which is equal to 100. Similarly, 10^3 is equal to 1000, and so on.
Step 2: Move the Decimal Point
Once you have identified the power of 10, the next step is to move the decimal point in the decimal number to the right by the number of places indicated by the exponent. For instance, if you have the decimal number 0.25 and you want to multiply it by 10^3, you would move the decimal point three places to the right, resulting in 250.
Step 3: Apply the Power of 10
After moving the decimal point, apply the power of 10 to the new number. In our previous example, we moved the decimal point three places to the right, so we now have 250. Since we multiplied by 10^3, we can write this as 250 10^3.
Step 4: Simplify the Expression
Finally, simplify the expression by combining the decimal number with the power of 10. In our example, 250 10^3 can be simplified to 250,000. This is because 10^3 is equal to 1000, and multiplying 250 by 1000 gives us 250,000.
Practical Examples
To further illustrate the concept, let’s look at a few practical examples:
1. Multiply 0.5 by 10^2.
– Move the decimal point two places to the right: 0.5 becomes 50.
– Apply the power of 10: 50 10^2 = 50 100 = 5,000.
2. Multiply 0.0003 by 10^5.
– Move the decimal point five places to the right: 0.0003 becomes 3.
– Apply the power of 10: 3 10^5 = 3 100,000 = 300,000.
3. Multiply 0.0123 by 10^-2.
– Move the decimal point two places to the left: 0.0123 becomes 0.00123.
– Apply the power of 10: 0.00123 10^-2 = 0.00123 0.01 = 0.0000123.
In conclusion, multiplying a decimal by a power of 10 involves identifying the power of 10, moving the decimal point accordingly, applying the power of 10, and simplifying the expression. By following these steps, you can easily multiply decimals by powers of 10 and apply this skill to various real-world scenarios.
