Problem 44
Question
\(5 \times 10^{4}-2 \times 10^{4}\)
Step-by-Step Solution
Verified Answer
30000
1Step 1: Identify the components
Separate and identify the components of the expression: 1. The first term: \( 5 \times 10^{4} \) 2. The second term: \( 2 \times 10^{4} \)
2Step 2: Simplify each term
Recognize that both terms have the same base of 10 raised to the power of 4. Thus, simplify each term with this understanding: 1. The first term: \( 5 \times 10^{4} = 50000 \) 2. The second term: \( 2 \times 10^{4} = 20000 \)
3Step 3: Subtract the simplified terms
Subtract the second term from the first term:\( 50000 - 20000 = 30000 \)
Key Concepts
scientific notationsubtraction of like termsbasic algebra steps
scientific notation
Scientific notation is a way of writing very large or very small numbers in a compact form using powers of ten. This is particularly useful in mathematics and science.
A number in scientific notation is expressed as the product of a number between 1 and 10 and a power of ten. For example, the number 50,000 can be written in scientific notation as \[ 5 \times 10^{4} \].
The notation consists of:
Changing these terms back to standard form (decimal form) can make subtraction or addition easier.
That's what we did in step 2 of the solution.
A number in scientific notation is expressed as the product of a number between 1 and 10 and a power of ten. For example, the number 50,000 can be written in scientific notation as \[ 5 \times 10^{4} \].
The notation consists of:
- A coefficient (a number between 1 and 10).
- A base of 10 raised to an exponent.
Changing these terms back to standard form (decimal form) can make subtraction or addition easier.
That's what we did in step 2 of the solution.
subtraction of like terms
Subtraction of like terms refers to subtracting numbers or expressions that have the same variables and powers.
Similar to grouping together similar items, like terms in algebra can be easily operated upon.
The exercise above uses like terms, so we can simplify and subtract them directly.
Both terms, \ 5\times10^{4} \ and \ 2\times 10^{4}, \ share the same base \({10}\) raised to the same power (\({4}\)).
This makes them perfect candidates for subtraction.
We simplify to:
Similar to grouping together similar items, like terms in algebra can be easily operated upon.
The exercise above uses like terms, so we can simplify and subtract them directly.
Both terms, \ 5\times10^{4} \ and \ 2\times 10^{4}, \ share the same base \({10}\) raised to the same power (\({4}\)).
This makes them perfect candidates for subtraction.
We simplify to:
- \({50000 - 20000 = 30000}\)
basic algebra steps
Basic algebra involves a series of fundamental steps to solve problems. Here, we break down the process:
In the given exercise, the steps were:
Finally, performing the basic operation (like subtraction) yields the solution.
By following these basic steps, algebraic expressions become easier to solve. Whether the problem involves scientific notation, like terms, or any other algebraic concept, these steps create a solid framework for solutions.
In the given exercise, the steps were:
- Identify and separate the components.
- Simplify each term (in standard form).
- Subtract the simplified terms.
Finally, performing the basic operation (like subtraction) yields the solution.
By following these basic steps, algebraic expressions become easier to solve. Whether the problem involves scientific notation, like terms, or any other algebraic concept, these steps create a solid framework for solutions.