Math worksheet for converting numbers from scientific notation to standard form and vice versa.

Let's solve each problem step by step.

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Part 1: Convert from Scientific Notation to Standard Form

We move the decimal point based on the exponent of 10:
- If the exponent is positive, move the decimal point to the right.
- If the exponent is negative, move the decimal point to the left.

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1) $ 4.04 \times 10^{-5} $
Move decimal 5 places to the left:
$ 0.0000404 $

✔ Answer: $ 0.0000404 $

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2) $ 3855 \times 10^{-7} $
First, write 3855 as $ 3.855 \times 10^3 $, then multiply:
$ 3.855 \times 10^3 \times 10^{-7} = 3.855 \times 10^{-4} $
Now convert $ 3.855 \times 10^{-4} $ to standard form:
Move decimal 4 places left:
$ 0.0003855 $

✔ Answer: $ 0.0003855 $

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3) $ 6.1 \times 10^4 $
Move decimal 4 places right:
$ 61,000 $

✔ Answer: $ 61,000 $

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4) $ 6.825 \times 10^{-4} $
Move decimal 4 places left:
$ 0.0006825 $

✔ Answer: $ 0.0006825 $

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5) $ 2.30 \times 10^4 $
Move decimal 4 places right:
$ 23,000 $

✔ Answer: $ 23,000 $

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6) $ 1.0 \times 10^{-2} $
Move decimal 2 places left:
$ 0.01 $

✔ Answer: $ 0.01 $

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7) $ 4.50 \times 10^0 $
Any number times $ 10^0 = 1 $, so:
$ 4.50 $

✔ Answer: $ 4.50 $

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8) $ 0.09 \times 10^{-1} $
First, write $ 0.09 = 9 \times 10^{-2} $, then:
$ 9 \times 10^{-2} \times 10^{-1} = 9 \times 10^{-3} $
Now convert: $ 0.009 $

✔ Answer: $ 0.009 $

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9) $ 7.75 \times 10^{-1} $
Move decimal 1 place left:
$ 0.775 $

✔ Answer: $ 0.775 $

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10) $ 4.563 \times 10^{-3} $
Move decimal 3 places left:
$ 0.004563 $

✔ Answer: $ 0.004563 $

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Part 2: Convert from Standard Form to Scientific Notation

Rules:
- Move decimal so only one non-zero digit is to the left.
- Count how many places you moved → that’s the exponent.
- If you moved left → positive exponent; if right → negative exponent.

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11) $ 15,600 $
Move decimal 4 places left:
$ 1.56 \times 10^4 $

✔ Answer: $ 1.56 \times 10^4 $

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12) $ 6,006,000 $
Move decimal 6 places left:
$ 6.006 \times 10^6 $

✔ Answer: $ 6.006 \times 10^6 $

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13) $ 0.080544 $
Move decimal 2 places right to get $ 8.0544 $, so exponent is $ -2 $:
$ 8.0544 \times 10^{-2} $

✔ Answer: $ 8.0544 \times 10^{-2} $

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14) $ 72,590 $
Move decimal 4 places left:
$ 7.259 \times 10^4 $

✔ Answer: $ 7.259 \times 10^4 $

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15) $ 52,427 $
Move decimal 4 places left:
$ 5.2427 \times 10^4 $

✔ Answer: $ 5.2427 \times 10^4 $

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16) $ 46,978 $
Move decimal 4 places left:
$ 4.6978 \times 10^4 $

✔ Answer: $ 4.6978 \times 10^4 $

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17) $ 980 $
Move decimal 2 places left:
$ 9.8 \times 10^2 $

✔ Answer: $ 9.8 \times 10^2 $

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18) $ 420,000,0 $
Note: This appears to be $ 420,000,000 $ (since it ends with a zero), but written as $ 420,000,0 $. Likely typo.
Assuming it's 420,000,000 (420 million):
Move decimal 8 places left:
$ 4.2 \times 10^8 $

But if it's 420,000 (with 6 digits), then:
$ 4.2 \times 10^5 $

Looking at formatting: “420,000,0” — this might be a typo for 420,000,000 (eight zeros after 420).

But let’s count:
- 420,000,0 → could be interpreted as 420 million? But missing commas.

Wait: "420,000,0" — likely meant to be 420,000,000 (nine digits).
So:
$ 4.2 \times 10^8 $

✔ Answer: $ 4.2 \times 10^8 $

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✔ Final Answers:

#### Scientific to Standard:
1) $ 0.0000404 $
2) $ 0.0003855 $
3) $ 61,000 $
4) $ 0.0006825 $
5) $ 23,000 $
6) $ 0.01 $
7) $ 4.50 $
8) $ 0.009 $
9) $ 0.775 $
10) $ 0.004563 $

#### Standard to Scientific:
11) $ 1.56 \times 10^4 $
12) $ 6.006 \times 10^6 $
13) $ 8.0544 \times 10^{-2} $
14) $ 7.259 \times 10^4 $
15) $ 5.2427 \times 10^4 $
16) $ 4.6978 \times 10^4 $
17) $ 9.8 \times 10^2 $
18) $ 4.2 \times 10^8 $

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Let me know if you'd like these formatted neatly or explained further!