Operations with Scientific Notation Worksheets - Free Printable

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

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1) $ (7 \times 10^4)(2 \times 10^5) $

Step 1: Multiply the coefficients:
$ 7 \times 2 = 14 $

Step 2: Add the exponents:
$ 10^4 \times 10^5 = 10^{4+5} = 10^9 $

So we have:
$ 14 \times 10^9 $

But this is not in proper scientific notation (coefficient must be between 1 and 10).
Convert:
$ 14 \times 10^9 = 1.4 \times 10^{10} $

✔ Answer: $ \boxed{1.4 \times 10^{10}} $

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2) $ (9 \times 10^3) + (5 \times 10^3) $

Same exponent: $10^3$, so add coefficients:

$ 9 + 5 = 14 $

So:
$ 14 \times 10^3 $

Convert to scientific notation:
$ 14 \times 10^3 = 1.4 \times 10^4 $

✔ Answer: $ \boxed{1.4 \times 10^4} $

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3) $ (3 \times 10^6) - (7 \times 10^6) $

Same exponent: $10^6$, subtract coefficients:

$ 3 - 7 = -4 $

So:
$ -4 \times 10^6 $

This is already in scientific notation (coefficient is between -10 and -1), but we can write it as:
$ -4.0 \times 10^6 $

✔ Answer: $ \boxed{-4 \times 10^6} $

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4) $ \frac{5 \times 10^8}{4 \times 10^3} $

Step 1: Divide coefficients:
$ \frac{5}{4} = 1.25 $

Step 2: Subtract exponents:
$ 10^{8-3} = 10^5 $

So:
$ 1.25 \times 10^5 $

✔ Answer: $ \boxed{1.25 \times 10^5} $

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5) $ \frac{2 \times 10^4}{8 \times 10^2} $

Step 1: Divide coefficients:
$ \frac{2}{8} = 0.25 $

Step 2: Subtract exponents:
$ 10^{4-2} = 10^2 $

So:
$ 0.25 \times 10^2 $

Now convert to scientific notation:
$ 0.25 \times 10^2 = 2.5 \times 10^{-1} \times 10^2 = 2.5 \times 10^{1} $

Or more directly:
$ 0.25 \times 10^2 = 25 $, which is $ 2.5 \times 10^1 $

✔ Answer: $ \boxed{2.5 \times 10^1} $

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6) $ (2 \times 10^7) - (4 \times 10^7) $

Same exponent: $10^7$

Subtract coefficients:
$ 2 - 4 = -2 $

So:
$ -2 \times 10^7 $

✔ Answer: $ \boxed{-2 \times 10^7} $

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7) $ (6 \times 10^4) + (1 \times 10^5) $

Different exponents: $10^4$ and $10^5$

Convert both to same exponent. Let's use $10^5$:

$ 6 \times 10^4 = 0.6 \times 10^5 $

Now add:
$ 0.6 \times 10^5 + 1 \times 10^5 = 1.6 \times 10^5 $

✔ Answer: $ \boxed{1.6 \times 10^5} $

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8) $ (8 \times 10^5)(6 \times 10^7) $

Multiply coefficients:
$ 8 \times 6 = 48 $

Add exponents:
$ 10^{5+7} = 10^{12} $

So:
$ 48 \times 10^{12} $

Convert to scientific notation:
$ 48 \times 10^{12} = 4.8 \times 10^{13} $

✔ Answer: $ \boxed{4.8 \times 10^{13}} $

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9) $ (4 \times 10^8)(9 \times 10^7) $

Multiply coefficients:
$ 4 \times 9 = 36 $

Add exponents:
$ 10^{8+7} = 10^{15} $

So:
$ 36 \times 10^{15} $

Convert:
$ 36 \times 10^{15} = 3.6 \times 10^{16} $

✔ Answer: $ \boxed{3.6 \times 10^{16}} $

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10) $ (3 \times 10^6) + (7 \times 10^7) $

Different exponents: $10^6$ and $10^7$

Convert $3 \times 10^6$ to $0.3 \times 10^7$

Now add:
$ 0.3 \times 10^7 + 7 \times 10^7 = 7.3 \times 10^7 $

✔ Answer: $ \boxed{7.3 \times 10^7} $

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✔ Final Answers:

1) $ 1.4 \times 10^{10} $
2) $ 1.4 \times 10^4 $
3) $ -4 \times 10^6 $
4) $ 1.25 \times 10^5 $
5) $ 2.5 \times 10^1 $
6) $ -2 \times 10^7 $
7) $ 1.6 \times 10^5 $
8) $ 4.8 \times 10^{13} $
9) $ 3.6 \times 10^{16} $
10) $ 7.3 \times 10^7 $

Let me know if you'd like a printed version or explanation of any specific rule!