Standard Form (A) Worksheet | Printable Maths Worksheets - Free Printable

Step-by-Step Solution:

To convert a number from standard form (scientific notation) to an ordinary number, you move the decimal point based on the power of 10.
* Positive Power ($10^n$): Move the decimal point $n$ places to the right. Add zeros if needed.
* Negative Power ($10^{-n}$): Move the decimal point $n$ places to the left. Add zeros before the number if needed.

Section A Calculations (Positive Powers):
1. $8.2 \times 10^4$: Move decimal 4 places right $\rightarrow$ 82,000
2. $9.1 \times 10^3$: Move decimal 3 places right $\rightarrow$ 9,100
3. $7.3 \times 10^2$: Move decimal 2 places right $\rightarrow$ 730
4. $6.5 \times 10^8$: Move decimal 8 places right $\rightarrow$ 650,000,000
5. $4.9 \times 10^4$: Move decimal 4 places right $\rightarrow$ 49,000
6. $5.6 \times 10^2$: Move decimal 2 places right $\rightarrow$ 560
7. $8.21 \times 10^3$: Move decimal 3 places right $\rightarrow$ 8,210
8. $6.13 \times 10^4$: Move decimal 4 places right $\rightarrow$ 61,300
9. $7.09 \times 10^8$: Move decimal 8 places right $\rightarrow$ 709,000,000
10. $5.345 \times 10^4$: Move decimal 4 places right $\rightarrow$ 53,450
11. $6.902 \times 10^3$: Move decimal 3 places right $\rightarrow$ 6,902
12. $2.003 \times 10^2$: Move decimal 2 places right $\rightarrow$ 200.3
13. $1.98 \times 10^8$: Move decimal 8 places right $\rightarrow$ 198,000,000
14. $4.012 \times 10^4$: Move decimal 4 places right $\rightarrow$ 40,120
15. $7.087 \times 10^2$: Move decimal 2 places right $\rightarrow$ 708.7
16. $8.5245 \times 10^9$: Move decimal 9 places right $\rightarrow$ 8,524,500,000
17. $7.6909 \times 10^7$: Move decimal 7 places right $\rightarrow$ 76,909,000
18. $7.1156 \times 10^8$: Move decimal 8 places right $\rightarrow$ 711,560,000

Section B Calculations (Negative Powers):
1. $8.2 \times 10^{-4}$: Move decimal 4 places left $\rightarrow$ 0.00082
2. $9.1 \times 10^{-3}$: Move decimal 3 places left $\rightarrow$ 0.0091
3. $7.3 \times 10^{-2}$: Move decimal 2 places left $\rightarrow$ 0.073
4. $6.5 \times 10^{-8}$: Move decimal 8 places left $\rightarrow$ 0.000000065
5. $4.9 \times 10^{-4}$: Move decimal 4 places left $\rightarrow$ 0.00049
6. $5.6 \times 10^{-2}$: Move decimal 2 places left $\rightarrow$ 0.056
7. $8.21 \times 10^{-3}$: Move decimal 3 places left $\rightarrow$ 0.00821
8. $4.62 \times 10^{-7}$: Move decimal 7 places left $\rightarrow$ 0.000000462
9. $8.03 \times 10^{-8}$: Move decimal 8 places left $\rightarrow$ 0.0000000803
10. $5.345 \times 10^{-4}$: Move decimal 4 places left $\rightarrow$ 0.0005345
11. $6.902 \times 10^{-3}$: Move decimal 3 places left $\rightarrow$ 0.006902
12. $2.003 \times 10^{-2}$: Move decimal 2 places left $\rightarrow$ 0.02003
13. $1.981 \times 10^{-8}$: Move decimal 8 places left $\rightarrow$ 0.00000001981
14. $4.012 \times 10^{-4}$: Move decimal 4 places left $\rightarrow$ 0.0004012
15. $7.087 \times 10^{-2}$: Move decimal 2 places left $\rightarrow$ 0.07087
16. $8.5245 \times 10^{-9}$: Move decimal 9 places left $\rightarrow$ 0.0000000085245
17. $7.6909 \times 10^{-7}$: Move decimal 7 places left $\rightarrow$ 0.00000076909
18. $7.1156 \times 10^{-8}$: Move decimal 8 places left $\rightarrow$ 0.000000071156

──────────────────────────────────────

Final Answer:
Section A
| Ordinary Number | Standard Form | | Ordinary Number | Standard Form |
| :--- | :--- | :--- | :--- | :--- |
| 82,000 | $8.2 \times 10^4$ | | 53,450 | $5.345 \times 10^4$ |
| 9,100 | $9.1 \times 10^3$ | | 6,902 | $6.902 \times 10^3$ |
| 730 | $7.3 \times 10^2$ | | 200.3 | $2.003 \times 10^2$ |
| 650,000,000 | $6.5 \times 10^8$ | | 198,000,000 | $1.98 \times 10^8$ |
| 49,000 | $4.9 \times 10^4$ | | 40,120 | $4.012 \times 10^4$ |
| 560 | $5.6 \times 10^2$ | | 708.7 | $7.087 \times 10^2$ |
| 8,210 | $8.21 \times 10^3$ | | 8,524,500,000 | $8.5245 \times 10^9$ |
| 61,300 | $6.13 \times 10^4$ | | 76,909,000 | $7.6909 \times 10^7$ |
| 709,000,000 | $7.09 \times 10^8$ | | 711,560,000 | $7.1156 \times 10^8$ |

Section B
| Ordinary Number | Standard Form | | Ordinary Number | Standard Form |
| :--- | :--- | :--- | :--- | :--- |
| 0.00082 | $8.2 \times 10^{-4}$ | | 0.0005345 | $5.345 \times 10^{-4}$ |
| 0.0091 | $9.1 \times 10^{-3}$ | | 0.006902 | $6.902 \times 10^{-3}$ |
| 0.073 | $7.3 \times 10^{-2}$ | | 0.02003 | $2.003 \times 10^{-2}$ |
| 0.000000065 | $6.5 \times 10^{-8}$ | | 0.00000001981 | $1.981 \times 10^{-8}$ |
| 0.00049 | $4.9 \times 10^{-4}$ | | 0.0004012 | $4.012 \times 10^{-4}$ |
| 0.056 | $5.6 \times 10^{-2}$ | | 0.07087 | $7.087 \times 10^{-2}$ |
| 0.00821 | $8.21 \times 10^{-3}$ | | 0.0000000085245 | $8.5245 \times 10^{-9}$ |
| 0.000000462 | $4.62 \times 10^{-7}$ | | 0.00000076909 | $7.6909 \times 10^{-7}$ |
| 0.0000000803 | $8.03 \times 10^{-8}$ | | 0.000000071156 | $7.1156 \times 10^{-8}$ |