Worksheet for practicing conversion of scientific notation to standard notation.

To solve this worksheet, we need to convert numbers from scientific notation into standard notation.

How it works:

Scientific notation looks like this:
> a × 10ⁿ

- If the exponent (the little number on top of 10) is positive, you move the decimal point in “a” to the right.
- If the exponent is negative, you move the decimal point to the left.
- You add zeros as needed.

Let’s go step by step for each problem:

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1) 4.7 × 10³
Exponent = +3 → Move decimal 3 places right → 4.7 → 47 → 470 → 4700
✔ Answer: 4700

2) 2 × 10¹
Exponent = +1 → Move decimal 1 place right → 2. → 20
✔ Answer: 20

3) 1.88 × 10²
Exponent = +2 → Move decimal 2 places right → 1.88 → 18.8 → 188
✔ Answer: 188

4) 4.9 × 10⁷
Exponent = +7 → Move decimal 7 places right → 4.9 → 49 → 490 → 4900 → 49000 → 490000 → 4900000 → 49000000
✔ Answer: 49,000,000

5) 3.875 × 10⁻⁵
Exponent = -5 → Move decimal 5 places left → 3.875 → 0.3875 → 0.03875 → 0.003875 → 0.0003875 → 0.00003875
✔ Answer: 0.00003875

6) 4.689 × 10⁻²
Exponent = -2 → Move decimal 2 places left → 4.689 → 0.4689 → 0.04689
✔ Answer: 0.04689

7) 3.199 × 10⁶
Exponent = +6 → Move decimal 6 places right → 3.199 → 31.99 → 319.9 → 3199 → 31990 → 319900 → 3199000
✔ Answer: 3,199,000

8) 6.12 × 10¹
Exponent = +1 → Move decimal 1 place right → 6.12 → 61.2
✔ Answer: 61.2

9) 9.23 × 10⁵
Exponent = +5 → Move decimal 5 places right → 9.23 → 92.3 → 923 → 9230 → 92300 → 923000
✔ Answer: 923,000

10) 4.25 × 10⁻⁴
Exponent = -4 → Move decimal 4 places left → 4.25 → 0.425 → 0.0425 → 0.00425 → 0.000425
✔ Answer: 0.000425

11) 6.34 × 10³
Exponent = +3 → Move decimal 3 places right → 6.34 → 63.4 → 634 → 6340
✔ Answer: 6,340

12) 2.04 × 10⁻⁴
Exponent = -4 → Move decimal 4 places left → 2.04 → 0.204 → 0.0204 → 0.00204 → 0.000204
✔ Answer: 0.000204

13) 1.04 × 10⁸
Exponent = +8 → Move decimal 8 places right → 1.04 → 10.4 → 104 → 1040 → 10400 → 104000 → 1040000 → 10400000 → 104000000
✔ Answer: 104,000,000

14) 9.172 × 10⁻⁵
Exponent = -5 → Move decimal 5 places left → 9.172 → 0.9172 → 0.09172 → 0.009172 → 0.0009172 → 0.00009172
✔ Answer: 0.00009172

15) 3.120 × 10⁻³
Exponent = -3 → Move decimal 3 places left → 3.120 → 0.3120 → 0.03120 → 0.003120 → which is 0.00312 (trailing zero doesn’t change value)
✔ Answer: 0.00312

16) 2.199 × 10⁷
Exponent = +7 → Move decimal 7 places right → 2.199 → 21.99 → 219.9 → 2199 → 21990 → 219900 → 2199000 → 21990000
✔ Answer: 21,990,000

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Final Answer:
1) 4700
2) 20
3) 188
4) 49000000
5) 0.00003875
6) 0.04689
7) 3199000
8) 61.2
9) 923000
10) 0.000425
11) 6340
12) 0.000204
13) 104000000
14) 0.00009172
15) 0.00312
16) 21990000