Addition and Subtraction with Scientific Notation worksheet from Kuta Software - Infinite Algebra 1.

Let's solve each problem step by step, simplifying the expressions and writing the answers in scientific notation.

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Key Concept:

To add or subtract numbers in scientific notation:
1. The powers of 10 must be the same.
2. If they are not the same, adjust one or both numbers so that they have the same exponent.
3. Then add or subtract the coefficients.
4. Rewrite the result in proper scientific notation (coefficient between 1 and 10).

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Problem 1:

$$
3.1 \times 10^3 + 4.3 \times 10^3
$$

Both have $10^3$, so add coefficients:

$$
(3.1 + 4.3) \times 10^3 = 7.4 \times 10^3
$$

✔ Answer: $7.4 \times 10^3$

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Problem 2:

$$
3 \times 10^1 + 6.4 \times 10^2
$$

Different exponents: $10^1$ vs $10^2$. Convert $3 \times 10^1$ to match $10^2$:

$$
3 \times 10^1 = 0.3 \times 10^2
$$

Now add:

$$
0.3 \times 10^2 + 6.4 \times 10^2 = (0.3 + 6.4) \times 10^2 = 6.7 \times 10^2
$$

✔ Answer: $6.7 \times 10^2$

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Problem 3:

$$
2.4 \times 10^4 + 5.57 \times 10^3
$$

Convert $5.57 \times 10^3$ to $10^4$:

$$
5.57 \times 10^3 = 0.557 \times 10^4
$$

Now add:

$$
2.4 \times 10^4 + 0.557 \times 10^4 = (2.4 + 0.557) \times 10^4 = 2.957 \times 10^4
$$

✔ Answer: $2.957 \times 10^4$

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Problem 4:

$$
5 \times 10^{-2} + 1.6 \times 10^{-3}
$$

Convert $1.6 \times 10^{-3}$ to $10^{-2}$:

$$
1.6 \times 10^{-3} = 0.16 \times 10^{-2}
$$

Now add:

$$
5 \times 10^{-2} + 0.16 \times 10^{-2} = (5 + 0.16) \times 10^{-2} = 5.16 \times 10^{-2}
$$

✔ Answer: $5.16 \times 10^{-2}$

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Problem 5:

$$
2.5 \times 10^1 + 6.14 \times 10^4
$$

Convert $2.5 \times 10^1$ to $10^4$:

$$
2.5 \times 10^1 = 0.025 \times 10^4
$$

Now add:

$$
0.025 \times 10^4 + 6.14 \times 10^4 = (0.025 + 6.14) \times 10^4 = 6.165 \times 10^4
$$

✔ Answer: $6.165 \times 10^4$

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Problem 6:

$$
7 \times 10^{-1} + 6.4 \times 10^{-5}
$$

Convert $6.4 \times 10^{-5}$ to $10^{-1}$:

$$
6.4 \times 10^{-5} = 0.000064 \times 10^{-1}
$$

Now add:

$$
7 \times 10^{-1} + 0.000064 \times 10^{-1} = (7 + 0.000064) \times 10^{-1} = 7.000064 \times 10^{-1}
$$

But this is not simplified. We need to write it properly.

Actually, since $7 \times 10^{-1} = 0.7$, and $6.4 \times 10^{-5} = 0.000064$, adding:

$$
0.7 + 0.000064 = 0.700064
$$

Now convert to scientific notation:

$$
0.700064 = 7.00064 \times 10^{-1}
$$

✔ Answer: $7.00064 \times 10^{-1}$

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Problem 7:

$$
5 \times 10^{-3} + 3.3 \times 10^{-6}
$$

Convert $3.3 \times 10^{-6}$ to $10^{-3}$:

$$
3.3 \times 10^{-6} = 0.0033 \times 10^{-3}
$$

Now add:

$$
5 \times 10^{-3} + 0.0033 \times 10^{-3} = (5 + 0.0033) \times 10^{-3} = 5.0033 \times 10^{-3}
$$

✔ Answer: $5.0033 \times 10^{-3}$

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Problem 8:

$$
8 \times 10^{-1} + 6.9 \times 10^3
$$

Convert $8 \times 10^{-1}$ to $10^3$:

$$
8 \times 10^{-1} = 0.8 \times 10^0 = 0.0008 \times 10^3
$$

Now add:

$$
0.0008 \times 10^3 + 6.9 \times 10^3 = (0.0008 + 6.9) \times 10^3 = 6.9008 \times 10^3
$$

✔ Answer: $6.9008 \times 10^3$

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✔ Final Answers:

1) $7.4 \times 10^3$
2) $6.7 \times 10^2$
3) $2.957 \times 10^4$
4) $5.16 \times 10^{-2}$
5) $6.165 \times 10^4$
6) $7.00064 \times 10^{-1}$
7) $5.0033 \times 10^{-3}$
8) $6.9008 \times 10^3$

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