Problem 45 - Elementary Algebra

Question

\(9 \times 10^{2}+5 \times 10^{2}\)

Step-by-Step Solution

Answer

1400

Step 1: Understand the Expression

The given expression is composed of two terms: \(9 \times 10^2\) and \(5 \times 10^2\). These are both scientific notations.

Step 2: Calculate Each Term

Calculate the value of each term separately. First, find the value of \(9 \times 10^2\): \(9 \times 100 = 900\).Next, find the value of \(5 \times 10^2\): \(5 \times 100 = 500\).

Step 3: Add the Results

Now, add the two values calculated in the previous step: \(900 + 500 = 1400\).

Key Concepts

Multiplication

When we talk about multiplication, we are discussing one of the basic operations in mathematics. This is the process of finding the product of two numbers. For example, if you multiply 3 by 4, you get 12. In our original exercise, we had to multiply the digits by a power of ten (which we will discuss separately). Remember:

• Multiplication is repeated addition. For instance, 3 multiplied by 4 is the same as adding 3 four times: 3 + 3 + 3 + 3 = 12.
• In our case, multiplying 9 by 100 means adding 9 one hundred times.

It helps to understand what each digit stands for and how multiplication affects each digit in the number.

Addition

Addition is another fundamental concept in mathematics. It is the process of calculating the total of two or more numbers or amounts. For example, 3 + 4 equals 7. In our exercise, after we calculated the value of each term, we had to add the values together:

• When adding 900 + 500, we first add the hundreds place: 9 hundreds + 5 hundreds = 14 hundreds.
• Thus, 900 + 500 equals 1400.

Addition helps in combining values to get a total. It is essential to align numbers by their place values (Hundreds, Tens, Units) to simplify addition.

Powers of Ten

Powers of ten are a way to express large numbers in a simplified form using exponents. The powers of ten concept is critical for scientific notation. Here’s a detailed breakdown:

• The power (or exponent) indicates how many times the number 10 is multiplied by itself.
• For example, in our exercise, the expression was given as 9 × 10^2 and 5 × 10^2.

The exponent 2 in the expression 10^2 means that 10 is multiplied by itself 2 times: 10 × 10 = 100. So:

• 9 × 10^2 translates to 9 × 100 = 900.
• Similarly, 5 × 10^2 translates to 5 × 100 = 500.

Understanding powers of ten makes it easier to handle large numbers and perform operations like multiplication and addition quickly.