Scientific Notation - Addition and Subtraction - Free Printable

Let's carefully go through the problem step by step and correctly solve:

We are given the expression:

$$
2.7 \times 10^6 + 5.8 \times 10^2
$$

Step 1: Identify the exponents

- The exponents are 6 and 2.
- The smaller exponent is 2, which is already correctly identified.

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Step 2: Subtract the smaller exponent from the larger one

$$
6 - 2 = 4
$$
This is correct — we get 4.

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Step 3: Multiply $10^2$ by $10^4$

We're told to "multiply $10^2$ by $10^4$", but let’s understand why.

To add numbers in scientific notation, they must have the same exponent. So we need to rewrite both numbers so they have the same power of 10.

We can either:
- Convert $2.7 \times 10^6$ to a form with $10^2$, or
- Convert $5.8 \times 10^2$ to a form with $10^6$

Since $10^6$ is larger, it's easier to convert the smaller number ($5.8 \times 10^2$) to match $10^6$.

So, we want to write $5.8 \times 10^2$ as something times $10^6$.

To do that, we multiply $10^2$ by $10^4$, because:
$$
10^2 \times 10^4 = 10^{2+4} = 10^6
$$

So:
$$
5.8 \times 10^2 = 5.8 \times 10^2 \times \frac{10^4}{10^4} = (5.8 \times 10^4) \times 10^2 \quad \text{(Wait — better way)}
$$

Actually, let's do this properly:

We want to express $5.8 \times 10^2$ in terms of $10^6$. That means we need to increase the exponent from 2 to 6, which requires multiplying by $10^4$.

But when we do that, we must divide the coefficient by $10^4$ to keep the value the same.

So:
$$
5.8 \times 10^2 = (5.8 \div 10^4) \times 10^6 = (0.00058) \times 10^6
$$

Now we can add:
$$
2.7 \times 10^6 + 0.00058 \times 10^6 = (2.7 + 0.00058) \times 10^6 = 2.70058 \times 10^6
$$

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Final Answer:

$$
\boxed{2.70058 \times 10^6}
$$

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Summary of Steps:

1. Smaller exponent: 2
2. Difference: $6 - 2 = 4$
3. Multiply $10^2$ by $10^4$ to make $10^6$
4. Adjust the coefficient: $5.8 \to 0.00058$
5. Add: $2.7 + 0.00058 = 2.70058$
6. Result: $\boxed{2.70058 \times 10^6}$

✔ So, the image is guiding you correctly through the steps — just remember that you’re converting the smaller term to match the larger exponent before adding.