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We are given the equation:

\[
(a \times 10^b) \times (5.3 \times 10^8) = 2.226 \times 10^4
\]

We need to find the values of \(a\) and \(b\), where \(a \times 10^b\) is in standard form.

### Step 1: Simplify the equation

First, rewrite the expression:

\[
(a \times 10^b) \times (5.3 \times 10^8) = 2.226 \times 10^4
\]

This can be factored as:

\[
a \times 5.3 \times 10^{b+8} = 2.226 \times 10^4
\]

### Step 2: Separate the powers of 10

Now, compare the powers of 10 on both sides of the equation. The left-hand side has the power of 10 as \(10^{b+8}\), and the right-hand side has \(10^4\). Therefore, we can equate the exponents:

\[
b + 8 = 4
\]

Solving this:

\[
b = 4 - 8 = -4
\]

### Step 3: Solve for \(a\)

Now, equate the numerical coefficients. On the left-hand side, we have:

\[
a \times 5.3 = 2.226
\]

Solve for \(a\):

\[
a = \frac{2.226}{5.3} \approx 0.42
\]

### Final answer:

\[
a = 0.42, \quad b = -4
\]

Would you like a detailed explanation of any specific step, or do you have further questions?

Here are 5 related questions:
1. How can you multiply two numbers in standard form?
2. What are the rules for adding exponents in scientific notation?
3. Why do we compare the powers of 10 directly in this type of equation?
4. How do you determine if a number is in standard form?
5. Can the value of \(a\) in standard form be less than 1?

**Tip:** In standard form, the number \(a\) must always lie between 1 and 10 (excluding 10). If it's not, adjust the exponent \(b\) accordingly.

(a × 10^b) × (5.3 × 10^8) = 2.226 × 10^4. Given that a × 10^b is in standard form, work out the values of a and b.

Work out the values of a and b from the equation (a × 10^b) × (5.3 × 10^8) = 2.226 × 10^4. Understand the steps to solve scientific notation problems using algebra and exponent rules. Suitable for Grades 9-10.

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