2.44×10^3 + 1.9×10^5
Understand the Problem
The question is asking us to perform the addition of two numbers expressed in scientific notation: 2.44×10^3 and 1.9×10^5. To solve this, we will first convert both numbers to the same exponent before adding them together.
Answer
$1.9244 \times 10^5$
Answer for screen readers
The answer is $1.9244 \times 10^5$.
Steps to Solve
- Convert to the Same Exponent
To add the two numbers in scientific notation, we first need to convert them to the same exponent. The exponents in our numbers are 3 and 5. We can convert $2.44 \times 10^3$ to have an exponent of 5.
To do this, we rewrite $2.44 \times 10^3$ as:
$$ 2.44 \times 10^3 = 2.44 \times 10^3 \times \frac{10^2}{10^2} = 2.44 \times 10^5 \times 10^{-2} = 0.0244 \times 10^5 $$
- Write Both Numbers with the Same Exponent
Now that we have both numbers with an exponent of 5, we can express them as:
$$ 0.0244 \times 10^5 $$
and
$$ 1.9 \times 10^5 $$
- Add the Converted Numbers
Now we can add the two numbers together:
$$ 0.0244 \times 10^5 + 1.9 \times 10^5 = (0.0244 + 1.9) \times 10^5 $$
Calculating this gives us:
$$ 1.9244 \times 10^5 $$
- Express in Proper Scientific Notation
The result $1.9244 \times 10^5$ is already in proper scientific notation, but we should ensure it is in standard form (the coefficient between 1 and 10). Since $1.9244$ is between 1 and 10, we keep it as it is.
The answer is $1.9244 \times 10^5$.
More Information
In scientific notation, we express very large or very small numbers in a standard form to keep calculations manageable. When adding numbers in scientific notation, it is critical to ensure they share the same exponent before proceeding with the addition.
Tips
- Failing to align the exponents correctly before adding. Always ensure that both terms have the same exponent.
- Miscalculating when converting the numbers to have the same exponent. Double-check your multiplication or division of powers of ten.
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