Scientific notation practice worksheet with problems to convert numbers to standard and scientific notation.

Let's solve this step-by-step. The worksheet has two parts:

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Part 1: Convert from Scientific Notation to Standard Form

We take each number in scientific notation (like $ a \times 10^n $) and convert it to standard form by moving the decimal point.

- If $ n $ is positive, move the decimal point n places to the right.
- If $ n $ is negative, move the decimal point n places to the left.

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#### Solutions for Part 1:

1) $ 5.2034 \times 10^8 $
→ Move decimal 8 places right:
$ 520,340,000 $

2) $ 1.59 \times 10^6 $
→ Move decimal 6 places right:
$ 1,590,000 $

3) $ 2.1631 \times 10^5 $
→ Move decimal 5 places right:
$ 216,310 $

4) $ 6.2801 \times 10^7 $
→ Move decimal 7 places right:
$ 62,801,000 $

5) $ 6.393 \times 10^2 $
→ Move decimal 2 places right:
$ 639.3 $

6) $ 5.4502 \times 10^2 $
→ Move decimal 2 places right:
$ 545.02 $

7) $ 9.883 \times 10^9 $
→ Move decimal 9 places right:
$ 9,883,000,000 $

8) $ 9.37 \times 10^5 $
→ Move decimal 5 places right:
$ 937,000 $

9) $ 4.6845 \times 10^3 $
→ Move decimal 3 places right:
$ 4,684.5 $

10) $ 4.63 \times 10^8 $
→ Move decimal 8 places right:
$ 463,000,000 $

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Part 2: Convert from Standard Form to Scientific Notation

We rewrite large numbers in the form $ a \times 10^n $, where:
- $ 1 \leq a < 10 $
- $ n $ is an integer

To do this:
- Move the decimal point so that only one non-zero digit is to the left of the decimal.
- Count how many places you moved the decimal → that’s the exponent $ n $.
- If you moved left, $ n $ is positive; if right, $ n $ is negative.

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#### Solutions for Part 2:

11) $ 14,660,000 $
→ Move decimal 7 places left: $ 1.466 \times 10^7 $

12) $ 65,980 $
→ Move decimal 4 places left: $ 6.598 \times 10^4 $

13) $ 50.2 $
→ Move decimal 1 place left: $ 5.02 \times 10^1 $

14) $ 36,200 $
→ Move decimal 4 places left: $ 3.62 \times 10^4 $

15) $ 1,993,000,000 $
→ Move decimal 9 places left: $ 1.993 \times 10^9 $

16) $ 4130 $
→ Move decimal 3 places left: $ 4.13 \times 10^3 $

17) $ 765,000 $
→ Move decimal 5 places left: $ 7.65 \times 10^5 $

18) $ 38.184 $
→ Move decimal 1 place left: $ 3.8184 \times 10^1 $

19) $ 4,470,000 $
→ Move decimal 6 places left: $ 4.47 \times 10^6 $

20) $ 37,082 $
→ Move decimal 4 places left: $ 3.7082 \times 10^4 $

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✔ Final Answers:

#### Part 1: Scientific Notation → Standard Form
1) 520,340,000
2) 1,590,000
3) 216,310
4) 62,801,000
5) 639.3
6) 545.02
7) 9,883,000,000
8) 937,000
9) 4,684.5
10) 463,000,000

#### Part 2: Standard Form → Scientific Notation
11) $ 1.466 \times 10^7 $
12) $ 6.598 \times 10^4 $
13) $ 5.02 \times 10^1 $
14) $ 3.62 \times 10^4 $
15) $ 1.993 \times 10^9 $
16) $ 4.13 \times 10^3 $
17) $ 7.65 \times 10^5 $
18) $ 3.8184 \times 10^1 $
19) $ 4.47 \times 10^6 $
20) $ 3.7082 \times 10^4 $

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