Problem 79 - Elementary Algebra

Question

\(9.3 \times 10^{3} \mathrm{~kg}+4.8 \times 10^{4} \mathrm{~kg}\)

Step-by-Step Solution

Answer

57300 kg or \(5.73 \times 10^{4} \mathrm{~kg}\)

Step 1 - Identify the Given Numbers

The given numbers are in scientific notation: \(9.3 \times 10^{3} \mathrm{~kg}\) and \(4.8 \times 10^{4} \mathrm{~kg}\).

Step 2 - Convert to Standard Notation

Convert each number to standard notation to simplify the addition. \(9.3 \times 10^{3} = 9300\) kg\(4.8 \times 10^{4} = 48000\) kg

Step 3 - Add the Numbers

Add the converted numbers: 9300 kg + 48000 kg = 57300 kg

Step 4 - Convert Back to Scientific Notation

Convert the result back to scientific notation if necessary. 57300 kg in scientific notation is \(5.73 \times 10^{4} \mathrm{~kg}\).

Key Concepts

Addition in Scientific Notation

Scientific notation is a way of writing very large or very small numbers in a compact form. It consists of a number between 1 and 10, multiplied by a power of 10.
When adding numbers in scientific notation, it is important to have the same power of 10 for both numbers. If the exponents are different, you need to adjust one or both numbers.
In our exercise, we have to add:
\(9.3 \times 10^{3} \text{ kg} + 4.8 \times 10^{4} \text{ kg}\).
Since the exponents are different (3 and 4), we convert these to standard notation first for simplicity.

Converting to Standard Notation

Converting from scientific notation to standard notation involves expanding the number.
For example:
\(9.3 \times 10^{3} \text{ kg}\) becomes 9300 kg and \(4.8 \times 10^{4} \text{ kg}\) becomes 48000 kg.
1. Multiply the coefficient (the number in front) by 10 raised to the power given.
2. \(9.3 \times 10^{3} = 9.3 \times 1000 = 9300 \text{ kg}\).
3. \(4.8 \times 10^{4} = 4.8 \times 10000 = 48000 \text{ kg}\).
Now, it is easier to add or subtract these numbers since they are in standard form.

Elementary Algebra

Elementary algebra helps with understanding and handling mathematical expressions.
In this case, we simply add the two numbers we converted to standard notation:
\( 9300 \text{ kg} + 48000 \text{ kg} = 57300 \text{ kg} \).
Next, we convert the sum back to scientific notation if required:

• First, write the number as a product of a number between 1 and 10 and an appropriate power of 10.
• \(57300 \text{ kg}\) can be written as \(5.73 \times 10^{4} \text{ kg}\).
• Here, you move the decimal point 4 places to the left, adjusting the power of 10 accordingly.