Write the following decimals in expanded form. $$ 642.835(6 imes 100)+(4 imes 10)+(2 imes 1)+(8 imes 0.1)+ $$ Four thousand fifty-three and two hundred sixty- $$ 4,053.269(4 imes 1,00)+(5 imes 10)+(3 imes 1)+ $$ $$ 9,615.243 $$

Question

Write the following decimals in expanded form. $$ 642.835(6 	imes 100)+(4 	imes 10)+(2 	imes 1)+(8 	imes 0.1)+ $$ Four thousand fifty-three and two hundred sixty- $$ 4,053.269(4 	imes 1,00)+(5 	imes 10)+(3 	imes 1)+ $$ $$ 9,615.243 $$

UpStudy AI · Accepted Answer

Certainly! Let's break down each of the given decimals into their expanded forms, showing the value of each digit based on its place value.

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### 1. **642.835**

$$
642.835 = (6 \times 100) + (4 \times 10) + (2 \times 1) + (8 \times 0.1) + (3 \times 0.01) + (5 \times 0.001)
$$

**Explanation:**
- **6** is in the **hundreds** place: $$6 \times 100 = 600$$
- **4** is in the **tens** place: $$4 \times 10 = 40$$
- **2** is in the **ones** place: $$2 \times 1 = 2$$
- **8** is in the **tenths** place: $$8 \times 0.1 = 0.8$$
- **3** is in the **hundredths** place: $$3 \times 0.01 = 0.03$$
- **5** is in the **thousandths** place: $$5 \times 0.001 = 0.005$$

---

### 2. **4,053.269**

$$
4,053.269 = (4 \times 1,000) + (0 \times 100) + (5 \times 10) + (3 \times 1) + (2 \times 0.1) + (6 \times 0.01) + (9 \times 0.001)
$$

**Explanation:**
- **4** is in the **thousands** place: $$4 \times 1,000 = 4,000$$
- **0** is in the **hundreds** place: $$0 \times 100 = 0$$
- **5** is in the **tens** place: $$5 \times 10 = 50$$
- **3** is in the **ones** place: $$3 \times 1 = 3$$
- **2** is in the **tenths** place: $$2 \times 0.1 = 0.2$$
- **6** is in the **hundredths** place: $$6 \times 0.01 = 0.06$$
- **9** is in the **thousandths** place: $$9 \times 0.001 = 0.009$$

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### 3. **9,615.243**

$$
9,615.243 = (9 \times 1,000) + (6 \times 100) + (1 \times 10) + (5 \times 1) + (2 \times 0.1) + (4 \times 0.01) + (3 \times 0.001)
$$

**Explanation:**
- **9** is in the **thousands** place: $$9 \times 1,000 = 9,000$$
- **6** is in the **hundreds** place: $$6 \times 100 = 600$$
- **1** is in the **tens** place: $$1 \times 10 = 10$$
- **5** is in the **ones** place: $$5 \times 1 = 5$$
- **2** is in the **tenths** place: $$2 \times 0.1 = 0.2$$
- **4** is in the **hundredths** place: $$4 \times 0.01 = 0.04$$
- **3** is in the **thousandths** place: $$3 \times 0.001 = 0.003$$

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**Summary of Expanded Forms:**

1. $$ \mathbf{642.835} $$
   $$
   = (6 \times 100) + (4 \times 10) + (2 \times 1) + (8 \times 0.1) + (3 \times 0.01) + (5 \times 0.001)
   $$

2. $$ \mathbf{4,053.269} $$
   $$
   = (4 \times 1,000) + (0 \times 100) + (5 \times 10) + (3 \times 1) + (2 \times 0.1) + (6 \times 0.01) + (9 \times 0.001)
   $$

3. $$ \mathbf{9,615.243} $$
   $$
   = (9 \times 1,000) + (6 \times 100) + (1 \times 10) + (5 \times 1) + (2 \times 0.1) + (4 \times 0.01) + (3 \times 0.001)
   $$

Feel free to ask if you need further clarification or additional examples!
Here are the decimals in their expanded forms: 1. **642.835** $$ = (6 \times 100) + (4 \times 10) + (2 \times 1) + (8 \times 0.1) + (3 \times 0.01) + (5 \times 0.001) $$ 2. **4,053.269** $$ = (4 \times 1,000) + (0 \times 100) + (5 \times 10) + (3 \times 1) + (2 \times 0.1) + (6 \times 0.01) + (9 \times 0.001) $$ 3. **9,615.243** $$ = (9 \times 1,000) + (6 \times 100) + (1 \times 10) + (5 \times 1) + (2 \times 0.1) + (4 \times 0.01) + (3 \times 0.001) $$

Write the following decimals in expanded form. \( 642.835(6 \times 100)+(4 \times 10)+(2 \times 1)+(8 \times 0.1)+ \) Four thousand fifty-three and two hundred sixty- \( 4,053.269(4 \times 1,00)+(5 \times 10)+(3 \times 1)+ \) \( 9,615.243 \)

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