Add And Subtract In Scientific Notation Worksheets [PDF] (8.EE.A.4 ... - Free Printable

Let's solve each problem step by step, following the rules for adding and subtracting numbers in scientific notation. The key idea is that you can only directly add or subtract the coefficients if the powers of 10 are the same. If they're different, you must adjust one or both numbers so their exponents match.

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Problem 1: Subtract

$$
3.24 \times 10^3 - 2.42 \times 10^3
$$

Both numbers have the same exponent ($10^3$), so we can subtract the coefficients:

$$
(3.24 - 2.42) \times 10^3 = 0.82 \times 10^3
$$

Now convert to proper scientific notation (coefficient between 1 and 10):

$$
0.82 \times 10^3 = 8.2 \times 10^2
$$

✔ Answer: $ \boxed{8.2 \times 10^2} $

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Problem 2: Add

$$
5.82 \times 10^4 + 6.32 \times 10^4
$$

Same exponent ($10^4$), so add coefficients:

$$
(5.82 + 6.32) \times 10^4 = 12.14 \times 10^4
$$

Convert to proper scientific notation:

$$
12.14 \times 10^4 = 1.214 \times 10^5
$$

Round to nearest thousandth (three decimal places):
1.214 is already at three decimal places → no change.

✔ Answer: $ \boxed{1.214 \times 10^5} $

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Problem 3: Subtract

$$
6.98 \times 10^{-7} - 1.17 \times 10^{-9}
$$

Different exponents: $-7$ vs $-9$. Let's make them the same.

Convert $1.17 \times 10^{-9}$ to the same power as $10^{-7}$:

$$
1.17 \times 10^{-9} = 0.0117 \times 10^{-7}
$$

Now subtract:

$$
6.98 \times 10^{-7} - 0.0117 \times 10^{-7} = (6.98 - 0.0117) \times 10^{-7} = 6.9683 \times 10^{-7}
$$

Round coefficient to nearest thousandth (three decimal places):

6.9683 → look at fourth digit (3 < 5), so round down → 6.968

✔ Answer: $ \boxed{6.968 \times 10^{-7}} $

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Problem 4: Add

$$
1.35 \times 10^6 + 4.23 \times 10^4
$$

Different exponents: $10^6$ vs $10^4$

Convert $4.23 \times 10^4$ to $10^6$:

$$
4.23 \times 10^4 = 0.0423 \times 10^6
$$

Now add:

$$
1.35 \times 10^6 + 0.0423 \times 10^6 = (1.35 + 0.0423) \times 10^6 = 1.3923 \times 10^6
$$

Round coefficient to nearest thousandth (three decimal places):

1.3923 → fourth digit is 3 (< 5), so round down → 1.392

✔ Answer: $ \boxed{1.392 \times 10^6} $

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✔ Final Answers:

1. $ 8.2 \times 10^2 $
2. $ 1.214 \times 10^5 $
3. $ 6.968 \times 10^{-7} $
4. $ 1.392 \times 10^6 $

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