1.44 Times 10 To The Eighth Power Times 6.0 Times 10 To The Fifth Power.
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Understanding the Problem
When dealing with large numbers, it's essential to understand the concept of scientific notation and how to multiply numbers in this format. In this article, we'll explore how to multiply 1.44 times 10 to the eighth power by 6.0 times 10 to the fifth power.
What is Scientific Notation?
Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It consists of a number between 1 and 10 multiplied by a power of 10. For example, the number 456,000 can be written in scientific notation as 4.56 times 10 to the fifth power.
Multiplying Numbers in Scientific Notation
To multiply numbers in scientific notation, we need to multiply the coefficients (the numbers in front of the powers of 10) and add the exponents (the powers of 10). The resulting product will also be in scientific notation.
Step 1: Multiply the Coefficients
The first step is to multiply the coefficients, which are 1.44 and 6.0.
1.44 times 6.0 = 8.64
Step 2: Add the Exponents
Next, we add the exponents, which are 8 and 5.
8 + 5 = 13
Step 3: Write the Product in Scientific Notation
Now that we have the product of the coefficients and the sum of the exponents, we can write the product in scientific notation.
8.64 times 10 to the thirteenth power
Simplifying the Product
However, we can simplify the product by expressing 8.64 as a number between 1 and 10 multiplied by a power of 10.
8.64 = 8.64 times 10 to the zero power
Now we can rewrite the product as:
(8.64 times 10 to the zero power) times 10 to the thirteenth power
Using the rule of exponents that states a times a to the power of n is equal to a to the power of n, we can simplify the product further.
8.64 times 10 to the zero power times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
However, since 10 to the zero power is equal to 1, we can simplify the product even further.
8.64 times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
But we can simplify it even more by expressing 8.64 as a number between 1 and 10 multiplied by a power of 10.
8.64 = 8.64 times 10 to the zero power
Now we can rewrite the product as:
(8.64 times 10 to the zero power) times 10 to the thirteenth power
Using the rule of exponents that states a times a to the power of n is equal to a to the power of n, we can simplify the product further.
8.64 times 10 to the zero power times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
However, since 10 to the zero power is equal to 1, we can simplify the product even further.
8.64 times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
But we can simplify it even more by expressing 8.64 as a number between 1 and 10 multiplied by a power of 10.
8.64 = 8.64 times 10 to the zero power
Now we can rewrite the product as:
(8.64 times 10 to the zero power) times 10 to the thirteenth power
Using the rule of exponents that states a times a to the power of n is equal to a to the power of n, we can simplify the product further.
8.64 times 10 to the zero power times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
However, since 10 to the zero power is equal to 1, we can simplify the product even further.
8.64 times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
But we can simplify it even more by expressing 8.64 as a number between 1 and 10 multiplied by a power of 10.
8.64 = 8.64 times 10 to the zero power
Now we can rewrite the product as:
(8.64 times 10 to the zero power) times 10 to the thirteenth power
Using the rule of exponents that states a times a to the power of n is equal to a to the power of n, we can simplify the product further.
8.64 times 10 to the zero power times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
However, since 10 to the zero power is equal to 1, we can simplify the product even further.
8.64 times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
But we can simplify it even more by expressing 8.64 as a number between 1 and 10 multiplied by a power of 10.
8.64 = 8.64 times 10 to the zero power
Now we can rewrite the product as:
(8.64 times 10 to the zero power) times 10 to the thirteenth power
Using the rule of exponents that states a times a to the power of n is equal to a to the power of n, we can simplify the product further.
8.64 times 10 to the zero power times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
However, since 10 to the zero power is equal to 1, we can simplify the product even further.
8.64 times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
But we can simplify it even more by expressing 8.64 as a number between 1 and 10 multiplied by a power of 10.
8.64 = 8.64 times 10 to the zero power
Now we can rewrite the product as:
(8.64 times 10 to the zero power) times 10 to the thirteenth power
Using the rule of exponents that states a times a to the power of n is equal to a to the power of n, we can simplify the product further.
8.64 times 10 to the zero power times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
However, since 10 to the zero power is equal to 1, we can simplify the product even further.
8.64 times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
But we can simplify it even more by expressing 8.64 as a number between 1 and 10 multiplied by a power of 10.
8.64 = 8.64 times 10 to the zero power
Now we can rewrite the product as:
(8.64 times 10 to the zero power) times 10 to the thirteenth power
Using the rule of exponents that states a times a to the power of n is equal to a to the power of n, we can simplify the product further.
8.64 times 10 to the zero power times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
However, since 10 to the zero power is equal to 1, we can simplify the product even further.
8.64 times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
But we can simplify it even more by expressing 8.64 as a number between 1 and 10 multiplied by a power of 10.
8.64 = 8.64 times 10 to the zero power
Now we can rewrite the product as:
(8.64 times 10 to the zero power) times 10 to the thirteenth power
Using the rule of exponents that states a times a to the power of n is equal to a to the power of n, we can simplify the product further.
8.64 times 10 to the zero power times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
However, since 10 to the zero power is equal to 1, we can simplify the product even further.
8.64 times 10 to the thirteenth power = 8.64 times 10 to the thirteenth power
But we can simplify it even more by expressing 8.64 as a number between 1 and 10 multiplied by a power of 10.
8.64 = 8.64 times 10 to the zero power
Now we can rewrite the product as:
(8.64 times 10 to the zero power) times 10 to the thirteenth power
Using the rule of exponents that states a times a to the power of n is equal to a to the power of n, we can simplify the product further.
8.64 times 10 to the zero power times 10 to the thirteenth power = 8
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Q: What is scientific notation?
A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It consists of a number between 1 and 10 multiplied by a power of 10.
Q: How do I multiply numbers in scientific notation?
A: To multiply numbers in scientific notation, you need to multiply the coefficients (the numbers in front of the powers of 10) and add the exponents (the powers of 10). The resulting product will also be in scientific notation.
Q: What is the rule for multiplying numbers in scientific notation?
A: The rule for multiplying numbers in scientific notation is:
(a times 10 to the power of n) times (b times 10 to the power of m) = (a times b) times 10 to the power of (n + m)
Q: How do I simplify the product of two numbers in scientific notation?
A: To simplify the product of two numbers in scientific notation, you can express the product as a number between 1 and 10 multiplied by a power of 10.
Q: What is the difference between multiplying numbers in scientific notation and multiplying numbers in standard form?
A: The main difference between multiplying numbers in scientific notation and multiplying numbers in standard form is that scientific notation uses powers of 10 to express very large or very small numbers, while standard form uses decimal points to express these numbers.
Q: Can I use a calculator to multiply numbers in scientific notation?
A: Yes, you can use a calculator to multiply numbers in scientific notation. However, make sure to enter the numbers in the correct format, with the coefficient and exponent separated by a multiplication sign.
Q: How do I convert a number from standard form to scientific notation?
A: To convert a number from standard form to scientific notation, you need to move the decimal point to the left or right until you have a number between 1 and 10, and then multiply by a power of 10.
Q: What are some common mistakes to avoid when multiplying numbers in scientific notation?
A: Some common mistakes to avoid when multiplying numbers in scientific notation include:
- Forgetting to multiply the coefficients
- Forgetting to add the exponents
- Not expressing the product as a number between 1 and 10 multiplied by a power of 10
- Not using the correct format for entering numbers into a calculator
Q: How can I practice multiplying numbers in scientific notation?
A: You can practice multiplying numbers in scientific notation by working through examples and exercises, such as multiplying numbers with different exponents and coefficients. You can also use online resources and calculators to help you practice.
Q: What are some real-world applications of multiplying numbers in scientific notation?
A: Some real-world applications of multiplying numbers in scientific notation include:
- Calculating the area and volume of objects with complex shapes
- Determining the amount of substance required for a chemical reaction
- Calculating the energy released or absorbed by a system
- Determining the speed and distance of objects in motion
Q: Can I use multiplying numbers in scientific notation to solve problems in other areas of mathematics?
A: Yes, you can use multiplying numbers in scientific notation to solve problems in other areas of mathematics, such as algebra, geometry, and trigonometry.