Standard Form worksheet for converting scientific notation to ordinary numbers, suitable for GCSE Foundation/Higher level math practice.

Problem Overview:

The task involves converting numbers from standard form (scientific notation) to ordinary form (decimal form). Standard form is expressed as \( a \times 10^n \), where \( a \) is a number between 1 and 10, and \( n \) is an integer.

Solution Approach:

1. Understanding Standard Form:
- 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.

2. Section A: Convert numbers with positive exponents.
3. Section B: Convert numbers with negative exponents.

Section A: Positive Exponents

#### Row 1: \( 8.2 \times 10^4 \)
- Move the decimal point 4 places to the right: \( 8.2 \rightarrow 82000 \).
- Answer: \( 82000 \).

#### Row 2: \( 9.1 \times 10^3 \)
- Move the decimal point 3 places to the right: \( 9.1 \rightarrow 9100 \).
- Answer: \( 9100 \).

#### Row 3: \( 7.3 \times 10^2 \)
- Move the decimal point 2 places to the right: \( 7.3 \rightarrow 730 \).
- Answer: \( 730 \).

#### Row 4: \( 6.5 \times 10^8 \)
- Move the decimal point 8 places to the right: \( 6.5 \rightarrow 650000000 \).
- Answer: \( 650000000 \).

#### Row 5: \( 4.9 \times 10^4 \)
- Move the decimal point 4 places to the right: \( 4.9 \rightarrow 49000 \).
- Answer: \( 49000 \).

#### Row 6: \( 5.6 \times 10^2 \)
- Move the decimal point 2 places to the right: \( 5.6 \rightarrow 560 \).
- Answer: \( 560 \).

#### Row 7: \( 8.21 \times 10^3 \)
- Move the decimal point 3 places to the right: \( 8.21 \rightarrow 8210 \).
- Answer: \( 8210 \).

#### Row 8: \( 6.13 \times 10^4 \)
- Move the decimal point 4 places to the right: \( 6.13 \rightarrow 61300 \).
- Answer: \( 61300 \).

#### Row 9: \( 7.09 \times 10^8 \)
- Move the decimal point 8 places to the right: \( 7.09 \rightarrow 709000000 \).
- Answer: \( 709000000 \).

#### Row 10: \( 5.345 \times 10^4 \)
- Move the decimal point 4 places to the right: \( 5.345 \rightarrow 53450 \).
- Answer: \( 53450 \).

#### Row 11: \( 6.902 \times 10^3 \)
- Move the decimal point 3 places to the right: \( 6.902 \rightarrow 6902 \).
- Answer: \( 6902 \).

#### Row 12: \( 2.003 \times 10^2 \)
- Move the decimal point 2 places to the right: \( 2.003 \rightarrow 200.3 \).
- Answer: \( 200.3 \).

#### Row 13: \( 1.98 \times 10^8 \)
- Move the decimal point 8 places to the right: \( 1.98 \rightarrow 198000000 \).
- Answer: \( 198000000 \).

#### Row 14: \( 4.012 \times 10^4 \)
- Move the decimal point 4 places to the right: \( 4.012 \rightarrow 40120 \).
- Answer: \( 40120 \).

#### Row 15: \( 7.087 \times 10^2 \)
- Move the decimal point 2 places to the right: \( 7.087 \rightarrow 708.7 \).
- Answer: \( 708.7 \).

#### Row 16: \( 8.5245 \times 10^9 \)
- Move the decimal point 9 places to the right: \( 8.5245 \rightarrow 8524500000 \).
- Answer: \( 8524500000 \).

#### Row 17: \( 7.6909 \times 10^7 \)
- Move the decimal point 7 places to the right: \( 7.6909 \rightarrow 76909000 \).
- Answer: \( 76909000 \).

#### Row 18: \( 7.1156 \times 10^8 \)
- Move the decimal point 8 places to the right: \( 7.1156 \rightarrow 711560000 \).
- Answer: \( 711560000 \).

Section B: Negative Exponents

#### Row 1: \( 8.2 \times 10^{-4} \)
- Move the decimal point 4 places to the left: \( 8.2 \rightarrow 0.00082 \).
- Answer: \( 0.00082 \).

#### Row 2: \( 9.1 \times 10^{-3} \)
- Move the decimal point 3 places to the left: \( 9.1 \rightarrow 0.0091 \).
- Answer: \( 0.0091 \).

#### Row 3: \( 7.3 \times 10^{-2} \)
- Move the decimal point 2 places to the left: \( 7.3 \rightarrow 0.073 \).
- Answer: \( 0.073 \).

#### Row 4: \( 6.5 \times 10^{-8} \)
- Move the decimal point 8 places to the left: \( 6.5 \rightarrow 0.000000065 \).
- Answer: \( 0.000000065 \).

#### Row 5: \( 4.9 \times 10^{-4} \)
- Move the decimal point 4 places to the left: \( 4.9 \rightarrow 0.00049 \).
- Answer: \( 0.00049 \).

#### Row 6: \( 5.6 \times 10^{-2} \)
- Move the decimal point 2 places to the left: \( 5.6 \rightarrow 0.056 \).
- Answer: \( 0.056 \).

#### Row 7: \( 8.21 \times 10^{-3} \)
- Move the decimal point 3 places to the left: \( 8.21 \rightarrow 0.00821 \).
- Answer: \( 0.00821 \).

#### Row 8: \( 4.62 \times 10^{-7} \)
- Move the decimal point 7 places to the left: \( 4.62 \rightarrow 0.000000462 \).
- Answer: \( 0.000000462 \).

#### Row 9: \( 8.03 \times 10^{-8} \)
- Move the decimal point 8 places to the left: \( 8.03 \rightarrow 0.0000000803 \).
- Answer: \( 0.0000000803 \).

#### Row 10: \( 5.345 \times 10^{-4} \)
- Move the decimal point 4 places to the left: \( 5.345 \rightarrow 0.0005345 \).
- Answer: \( 0.0005345 \).

#### Row 11: \( 6.902 \times 10^{-3} \)
- Move the decimal point 3 places to the left: \( 6.902 \rightarrow 0.006902 \).
- Answer: \( 0.006902 \).

#### Row 12: \( 2.003 \times 10^{-2} \)
- Move the decimal point 2 places to the left: \( 2.003 \rightarrow 0.02003 \).
- Answer: \( 0.02003 \).

#### Row 13: \( 1.981 \times 10^{-8} \)
- Move the decimal point 8 places to the left: \( 1.981 \rightarrow 0.00000001981 \).
- Answer: \( 0.00000001981 \).

#### Row 14: \( 4.012 \times 10^{-4} \)
- Move the decimal point 4 places to the left: \( 4.012 \rightarrow 0.0004012 \).
- Answer: \( 0.0004012 \).

#### Row 15: \( 7.087 \times 10^{-2} \)
- Move the decimal point 2 places to the left: \( 7.087 \rightarrow 0.07087 \).
- Answer: \( 0.07087 \).

#### Row 16: \( 8.5245 \times 10^{-9} \)
- Move the decimal point 9 places to the left: \( 8.5245 \rightarrow 0.0000000085245 \).
- Answer: \( 0.0000000085245 \).

#### Row 17: \( 7.6909 \times 10^{-7} \)
- Move the decimal point 7 places to the left: \( 7.6909 \rightarrow 0.00000076909 \).
- Answer: \( 0.00000076909 \).

#### Row 18: \( 7.1156 \times 10^{-8} \)
- Move the decimal point 8 places to the left: \( 7.1156 \rightarrow 0.000000071156 \).
- Answer: \( 0.000000071156 \).

Final Answer:

\[
\boxed{
\begin{array}{c|c}
\text{Section A} & \text{Section B} \\
\hline
82000 & 0.00082 \\
9100 & 0.0091 \\
730 & 0.073 \\
650000000 & 0.000000065 \\
49000 & 0.00049 \\
560 & 0.056 \\
8210 & 0.00821 \\
61300 & 0.000000462 \\
709000000 & 0.0000000803 \\
53450 & 0.0005345 \\
6902 & 0.006902 \\
200.3 & 0.02003 \\
198000000 & 0.00000001981 \\
40120 & 0.0004012 \\
708.7 & 0.07087 \\
8524500000 & 0.0000000085245 \\
76909000 & 0.00000076909 \\
711560000 & 0.000000071156 \\
\end{array}
}
\]