Practice sheet for converting expanded notation expressions into standard numerical form, including decimal place values.

Let's solve each problem step by step and write the numbers in standard form (i.e., regular decimal notation). We'll break down each expression based on place value.

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Problem 1:

$$
(9 \times 100) + (1 \times 10) + (2 \times 1) + (8 \times \frac{1}{10}) + (3 \times \frac{1}{100}) + (7 \times \frac{1}{1000}) + (5 \times \frac{1}{10000}) + (4 \times \frac{1}{100000})
$$

Break it down:
- $9 \times 100 = 900$
- $1 \times 10 = 10$
- $2 \times 1 = 2$
- $8 \times \frac{1}{10} = 0.8$
- $3 \times \frac{1}{100} = 0.03$
- $7 \times \frac{1}{1000} = 0.007$
- $5 \times \frac{1}{10000} = 0.0005$
- $4 \times \frac{1}{100000} = 0.00004$

Now add them:
$$
900 + 10 + 2 + 0.8 + 0.03 + 0.007 + 0.0005 + 0.00004 = 912.837504
$$

✔ Answer: 912.837504

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Problem 2:

$$
(8 \times 100) + (1 \times 10) + (6 \times \frac{1}{10}) + (2 \times \frac{1}{100}) + (3 \times \frac{1}{1000}) + (5 \times \frac{1}{10000})
$$

Break it down:
- $8 \times 100 = 800$
- $1 \times 10 = 10$
- $6 \times \frac{1}{10} = 0.6$
- $2 \times \frac{1}{100} = 0.02$
- $3 \times \frac{1}{1000} = 0.003$
- $5 \times \frac{1}{10000} = 0.0005$

Add:
$$
800 + 10 + 0.6 + 0.02 + 0.003 + 0.0005 = 810.6235
$$

✔ Answer: 810.6235

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Problem 3:

$$
(6 \times 10) + (4 \times 1) + (9 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (8 \times \frac{1}{10000})
$$

Break it down:
- $6 \times 10 = 60$
- $4 \times 1 = 4$
- $9 \times \frac{1}{10} = 0.9$
- $1 \times \frac{1}{100} = 0.01$
- $8 \times \frac{1}{10000} = 0.0008$

Add:
$$
60 + 4 + 0.9 + 0.01 + 0.0008 = 64.9108
$$

✔ Answer: 64.9108

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Problem 4:

$$
(1 \times 10) + (6 \times \frac{1}{10}) + (2 \times \frac{1}{100}) + (9 \times \frac{1}{1000}) + (4 \times \frac{1}{10000}) + (8 \times \frac{1}{100000}) + (1 \times \frac{1}{1000000})
$$

Break it down:
- $1 \times 10 = 10$
- $6 \times \frac{1}{10} = 0.6$
- $2 \times \frac{1}{100} = 0.02$
- $9 \times \frac{1}{1000} = 0.009$
- $4 \times \frac{1}{10000} = 0.0004$
- $8 \times \frac{1}{100000} = 0.00008$
- $1 \times \frac{1}{1000000} = 0.000001$

Add:
$$
10 + 0.6 + 0.02 + 0.009 + 0.0004 + 0.00008 + 0.000001 = 10.629481
$$

✔ Answer: 10.629481

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Problem 5:

$$
(4 \times 1) + (5 \times \frac{1}{10}) + (2 \times \frac{1}{1000}) + (9 \times \frac{1}{10000}) + (7 \times \frac{1}{100000})
$$

Break it down:
- $4 \times 1 = 4$
- $5 \times \frac{1}{10} = 0.5$
- $2 \times \frac{1}{1000} = 0.002$
- $9 \times \frac{1}{10000} = 0.0009$
- $7 \times \frac{1}{100000} = 0.00007$

Add:
$$
4 + 0.5 + 0.002 + 0.0009 + 0.00007 = 4.50297
$$

✔ Answer: 4.50297

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Problem 6:

$$
(3 \times 100) + (6 \times 10) + (9 \times 1) + (7 \times \frac{1}{10}) + (4 \times \frac{1}{100}) + (1 \times \frac{1}{1000}) + (2 \times \frac{1}{10000}) + (5 \times \frac{1}{100000})
$$

Break it down:
- $3 \times 100 = 300$
- $6 \times 10 = 60$
- $9 \times 1 = 9$
- $7 \times \frac{1}{10} = 0.7$
- $4 \times \frac{1}{100} = 0.04$
- $1 \times \frac{1}{1000} = 0.001$
- $2 \times \frac{1}{10000} = 0.0002$
- $5 \times \frac{1}{100000} = 0.00005$

Add:
$$
300 + 60 + 9 + 0.7 + 0.04 + 0.001 + 0.0002 + 0.00005 = 369.74125
$$

✔ Answer: 369.74125

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Problem 7:

$$
(5 \times 10) + (1 \times 1) + (3 \times \frac{1}{10}) + (6 \times \frac{1}{100})
$$

Break it down:
- $5 \times 10 = 50$
- $1 \times 1 = 1$
- $3 \times \frac{1}{10} = 0.3$
- $6 \times \frac{1}{100} = 0.06$

Add:
$$
50 + 1 + 0.3 + 0.06 = 51.36
$$

✔ Answer: 51.36

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Problem 8:

$$
(2 \times 1) + (3 \times \frac{1}{10}) + (5 \times \frac{1}{100}) + (8 \times \frac{1}{1000}) + (6 \times \frac{1}{10000}) + (4 \times \frac{1}{100000})
$$

Break it down:
- $2 \times 1 = 2$
- $3 \times \frac{1}{10} = 0.3$
- $5 \times \frac{1}{100} = 0.05$
- $8 \times \frac{1}{1000} = 0.008$
- $6 \times \frac{1}{10000} = 0.0006$
- $4 \times \frac{1}{100000} = 0.00004$

Add:
$$
2 + 0.3 + 0.05 + 0.008 + 0.0006 + 0.00004 = 2.35864
$$

✔ Answer: 2.35864

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✔ Final Answers:

1. 912.837504
2. 810.6235
3. 64.9108
4. 10.629481
5. 4.50297
6. 369.74125
7. 51.36
8. 2.35864

These are all in standard form (decimal notation), as required.

Let me know if you'd like a printed version or explanation for any specific one!