How to multiply standard form
The standard form, also known as scientific notation, is a way to represent very large or very small numbers using a combination of a decimal number and a power of 10. It is commonly used in scientific and engineering fields where precision is essential. Multiplying numbers in standard form may seem challenging at first, but with the right approach, it can be simplified.
To multiply numbers in standard form, you need to follow a specific process. The first step is to multiply the decimal numbers together. Then, add the powers of 10. If the powers have the same sign, you add them together. However, if the powers have different signs, you subtract the smaller power from the larger one.
Let’s say you have two numbers written in standard form: (a times 10^n) and (b times 10^m). To multiply them, you would multiply the decimal parts: (a times b). Then, add the powers of 10: (10^n times 10^m). Simplify the result further if necessary by adjusting the power of 10.
By following these steps, you will be able to multiply numbers written in standard form accurately and efficiently. Practice with various examples to strengthen your understanding and improve your skills in working with these types of numbers. So let’s dive in and explore the world of multiplying standard form numbers!
Step 1: Multiply the Coefficients
In order to multiply numbers in standard form, the first step is to multiply the coefficients.
Let’s consider two numbers in standard form: a x 10m and b x 10n.
The coefficients, a and b, are the numbers that are multiplied together to get the new coefficient.
To do this, simply multiply the values of a and b.
For example, if we have 3 x 104 and 2 x 102, we would multiply the coefficients:
3 × 2 = 6.
So, in this case, the new coefficient would be 6.
Now you know how to multiply the coefficients in standard form!
Next Steps
Once you have multiplied the coefficients, you will need to multiply the powers of 10.
Continue reading to learn more about Step 2: Multiply the Powers of 10.
Step 2: Add the exponents
Once you have rewritten both numbers in standard form, it’s time to add the exponents. This step is crucial because the exponents determine the magnitude of the numbers.
Let’s take an example to understand how to add the exponents:
Example:
Suppose you have the following numbers: 3.2 x 10^4 and 1.5 x 10^3.
To multiply these numbers, you need to add the exponents (4 + 3 = 7) and keep the base unchanged (3.2 x 1.5). The result would be:
4.8 x 10^7.
By adding the exponents, we can see that the product of these numbers is a much larger number than either of the two multiplicands.
Rules for adding exponents:
1. When multiplying two numbers in standard form, first multiply the base numbers and then add the exponents.
2. If the base numbers are different, the exponents cannot be added.
3. Keep the base number unchanged when adding the exponents.
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