Math worksheet for converting scientific notation to standard form and vice versa.
Worksheet titled "Converting Scientific Notation" with exercises to convert numbers between scientific and standard forms, including numbered problems and answer spaces.
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Show Answer Key & Explanations
Step-by-step solution for: Worksheets | Free - Distance Learning, worksheets and more ...
Let's solve each problem step by step.
---
We move the decimal point according to 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.
---
1) $ 4.83 \times 10^1 $
Move decimal 1 place right:
$ 4.83 \rightarrow 48.3 $
✔ Answer: 48.3
---
2) $ 9 \times 10^1 $
Move decimal 1 place right:
$ 9 \rightarrow 90 $
✔ Answer: 90
---
3) $ 8.2 \times 10^0 $
Any number × $ 10^0 = $ itself (since $ 10^0 = 1 $):
$ 8.2 \times 1 = 8.2 $
✔ Answer: 8.2
---
4) $ 8.291 \times 10^3 $
Move decimal 3 places right:
$ 8.291 \rightarrow 8291 $
✔ Answer: 8,291
---
5) $ 1.939 \times 10^1 $
Move decimal 1 place right:
$ 1.939 \rightarrow 19.39 $
✔ Answer: 19.39
---
6) $ 3.4 \times 10^1 $
Move decimal 1 place right:
$ 3.4 \rightarrow 34 $
✔ Answer: 34
---
7) $ 4.37 \times 10^0 $
$ 10^0 = 1 $ → stays same:
✔ Answer: 4.37
---
8) $ 1 \times 10^5 $
Move decimal 5 places right:
$ 1 \rightarrow 100,000 $
✔ Answer: 100,000
---
9) $ 4 \times 10^0 $
$ 10^0 = 1 $ → $ 4 \times 1 = 4 $
✔ Answer: 4
---
10) $ 1.9 \times 10^6 $
Move decimal 6 places right:
$ 1.9 \rightarrow 1,900,000 $
✔ Answer: 1,900,000
---
Scientific notation format: $ a \times 10^n $, where $ 1 \leq a < 10 $
We move the decimal so that only one non-zero digit is to the left of the decimal, then count how many places we moved it (this becomes the exponent).
---
11) 8.58
Already between 1 and 10 → no need to move decimal:
$ 8.58 = 8.58 \times 10^0 $
✔ Answer: $ 8.58 \times 10^0 $
---
12) 0.0000076
Move decimal to the right until one non-zero digit is left:
0.0000076 → 7.6 (moved 6 places right)
So, $ 7.6 \times 10^{-6} $
✔ Answer: $ 7.6 \times 10^{-6} $
---
13) 0.0000038
Move decimal 6 places right:
0.0000038 → 3.8
So, $ 3.8 \times 10^{-6} $
✔ Answer: $ 3.8 \times 10^{-6} $
---
14) 0.0002829
Move decimal 4 places right:
0.0002829 → 2.829
So, $ 2.829 \times 10^{-4} $
✔ Answer: $ 2.829 \times 10^{-4} $
---
15) 2.55
Already in correct form:
$ 2.55 = 2.55 \times 10^0 $
✔ Answer: $ 2.55 \times 10^0 $
---
16) 980,000
Move decimal to left until one digit is left:
980,000 → 9.8 (moved 5 places left)
So, $ 9.8 \times 10^5 $
✔ Answer: $ 9.8 \times 10^5 $
---
17) 0.7
Move decimal 1 place right to get 7.0 → so $ 7.0 \times 10^{-1} $
✔ Answer: $ 7.0 \times 10^{-1} $
---
18) 11,800
Move decimal 3 places left:
11,800 → 1.18 (moved 4 places)
So, $ 1.18 \times 10^4 $
✔ Answer: $ 1.18 \times 10^4 $
---
19) 0.0764
Move decimal 2 places right:
0.0764 → 7.64 (moved 2 places)
So, $ 7.64 \times 10^{-2} $
✔ Answer: $ 7.64 \times 10^{-2} $
---
20) 0.000044
Move decimal 5 places right:
0.000044 → 4.4
So, $ 4.4 \times 10^{-5} $
✔ Answer: $ 4.4 \times 10^{-5} $
---
| # | Answer |
|---|--------|
| 1 | 48.3 |
| 2 | 90 |
| 3 | 8.2 |
| 4 | 8,291 |
| 5 | 19.39 |
| 6 | 34 |
| 7 | 4.37 |
| 8 | 100,000 |
| 9 | 4 |
| 10 | 1,900,000 |
| 11 | $ 8.58 \times 10^0 $ |
| 12 | $ 7.6 \times 10^{-6} $ |
| 13 | $ 3.8 \times 10^{-6} $ |
| 14 | $ 2.829 \times 10^{-4} $ |
| 15 | $ 2.55 \times 10^0 $ |
| 16 | $ 9.8 \times 10^5 $ |
| 17 | $ 7.0 \times 10^{-1} $ |
| 18 | $ 1.18 \times 10^4 $ |
| 19 | $ 7.64 \times 10^{-2} $ |
| 20 | $ 4.4 \times 10^{-5} $ |
Let me know if you'd like this formatted as a printable answer sheet!
---
Part 1: Convert from Scientific Notation to Standard Form
We move the decimal point according to 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.
---
1) $ 4.83 \times 10^1 $
Move decimal 1 place right:
$ 4.83 \rightarrow 48.3 $
✔ Answer: 48.3
---
2) $ 9 \times 10^1 $
Move decimal 1 place right:
$ 9 \rightarrow 90 $
✔ Answer: 90
---
3) $ 8.2 \times 10^0 $
Any number × $ 10^0 = $ itself (since $ 10^0 = 1 $):
$ 8.2 \times 1 = 8.2 $
✔ Answer: 8.2
---
4) $ 8.291 \times 10^3 $
Move decimal 3 places right:
$ 8.291 \rightarrow 8291 $
✔ Answer: 8,291
---
5) $ 1.939 \times 10^1 $
Move decimal 1 place right:
$ 1.939 \rightarrow 19.39 $
✔ Answer: 19.39
---
6) $ 3.4 \times 10^1 $
Move decimal 1 place right:
$ 3.4 \rightarrow 34 $
✔ Answer: 34
---
7) $ 4.37 \times 10^0 $
$ 10^0 = 1 $ → stays same:
✔ Answer: 4.37
---
8) $ 1 \times 10^5 $
Move decimal 5 places right:
$ 1 \rightarrow 100,000 $
✔ Answer: 100,000
---
9) $ 4 \times 10^0 $
$ 10^0 = 1 $ → $ 4 \times 1 = 4 $
✔ Answer: 4
---
10) $ 1.9 \times 10^6 $
Move decimal 6 places right:
$ 1.9 \rightarrow 1,900,000 $
✔ Answer: 1,900,000
---
Part 2: Convert from Standard Form to Scientific Notation
Scientific notation format: $ a \times 10^n $, where $ 1 \leq a < 10 $
We move the decimal so that only one non-zero digit is to the left of the decimal, then count how many places we moved it (this becomes the exponent).
---
11) 8.58
Already between 1 and 10 → no need to move decimal:
$ 8.58 = 8.58 \times 10^0 $
✔ Answer: $ 8.58 \times 10^0 $
---
12) 0.0000076
Move decimal to the right until one non-zero digit is left:
0.0000076 → 7.6 (moved 6 places right)
So, $ 7.6 \times 10^{-6} $
✔ Answer: $ 7.6 \times 10^{-6} $
---
13) 0.0000038
Move decimal 6 places right:
0.0000038 → 3.8
So, $ 3.8 \times 10^{-6} $
✔ Answer: $ 3.8 \times 10^{-6} $
---
14) 0.0002829
Move decimal 4 places right:
0.0002829 → 2.829
So, $ 2.829 \times 10^{-4} $
✔ Answer: $ 2.829 \times 10^{-4} $
---
15) 2.55
Already in correct form:
$ 2.55 = 2.55 \times 10^0 $
✔ Answer: $ 2.55 \times 10^0 $
---
16) 980,000
Move decimal to left until one digit is left:
980,000 → 9.8 (moved 5 places left)
So, $ 9.8 \times 10^5 $
✔ Answer: $ 9.8 \times 10^5 $
---
17) 0.7
Move decimal 1 place right to get 7.0 → so $ 7.0 \times 10^{-1} $
✔ Answer: $ 7.0 \times 10^{-1} $
---
18) 11,800
Move decimal 3 places left:
11,800 → 1.18 (moved 4 places)
So, $ 1.18 \times 10^4 $
✔ Answer: $ 1.18 \times 10^4 $
---
19) 0.0764
Move decimal 2 places right:
0.0764 → 7.64 (moved 2 places)
So, $ 7.64 \times 10^{-2} $
✔ Answer: $ 7.64 \times 10^{-2} $
---
20) 0.000044
Move decimal 5 places right:
0.000044 → 4.4
So, $ 4.4 \times 10^{-5} $
✔ Answer: $ 4.4 \times 10^{-5} $
---
✔ Final Answers:
| # | Answer |
|---|--------|
| 1 | 48.3 |
| 2 | 90 |
| 3 | 8.2 |
| 4 | 8,291 |
| 5 | 19.39 |
| 6 | 34 |
| 7 | 4.37 |
| 8 | 100,000 |
| 9 | 4 |
| 10 | 1,900,000 |
| 11 | $ 8.58 \times 10^0 $ |
| 12 | $ 7.6 \times 10^{-6} $ |
| 13 | $ 3.8 \times 10^{-6} $ |
| 14 | $ 2.829 \times 10^{-4} $ |
| 15 | $ 2.55 \times 10^0 $ |
| 16 | $ 9.8 \times 10^5 $ |
| 17 | $ 7.0 \times 10^{-1} $ |
| 18 | $ 1.18 \times 10^4 $ |
| 19 | $ 7.64 \times 10^{-2} $ |
| 20 | $ 4.4 \times 10^{-5} $ |
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of math worksheet scientific notation.
