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- \( 4,053.269(4 \times 1,00)+(5 \times 10)+(3 \times 1)+ \) \( 9,615.243 \)

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. --- ### 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: \(9 \times 0.001 = 0.009\) --- ### 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: \(3 \times 0.001 = 0.003\) --- **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!