Complete: a) \( 3 \times 10^{5}= \) \( \qquad \) b) \( 7 \times 10^{5}=7 \times \) \( \qquad \) \( \times \) \( \qquad \) x ...... \( x \) \( \qquad \) \( \times \) \( \qquad \) c) \( 5 \times 10^{7}= \) \( \qquad \) d) \( 8 \times 10^{6}= \) \( \qquad \) \( x \). \( \qquad \) x.. \( \qquad \) x. \( \qquad \) \( x \). \( \qquad \) \( x \). \( \qquad \) \( \times \). Write each of the following numbers in expanded form. \[ 9432127=\ldots \ldots \times 10^{5}+\ldots \ldots \times 10^{5}+\ldots \ldots \times 10^{4}+\ldots \ldots \times 10^{3}+\ldots \ldots \times 10^{2}+\ldots \ldots \times 10^{1}+\ldots \ldots \] Write in short form. \[ \begin{array}{l} 3 \times 10^{5}+4 \times 10^{5}+6 \times 10^{4}+9 \times 10^{3}+8 \times 10^{2}+2 \times 10+7= \\ 8 \times 10^{7}+4 \times 10^{5}+2 \times 10^{4}+6 \times 10^{2}+7 \times 10+3=\ldots \ldots \ldots \\ 4 \times 10^{5}+6 \times 10+7 \times 10^{8}+3 \times 10^{2}+5 \times 10^{6}+8 \times 10^{4}=\ldots \end{array} \]

Sure, let's complete each part step by step. ### a) \( 3 \times 10^{5} \) \[ 3 \times 10^{5} = 300,\!000 \] ### b) \( 7 \times 10^{5} \) \[ 7 \times 10^{5} = 700,\!000 \] ### c) \( 5 \times 10^{7} \) \[ 5 \times 10^{7} = 50,\!000,\!000 \] ### d) \( 8 \times 10^{6} \) \[ 8 \times 10^{6} = 8,\!000,\!000 \] --- ### Expanded Form of 9,432,127 To write the number \( 9,\!432,\!127 \) in expanded form, break it down by each digit's place value: \[ 9,\!432,\!127 = 9 \times 10^{6} + 4 \times 10^{5} + 3 \times 10^{4} + 2 \times 10^{3} + 1 \times 10^{2} + 2 \times 10^{1} + 7 \times 10^{0} \] Which simplifies to: \[ 9,\!432,\!127 = 9,000,000 + 400,000 + 30,000 + 2,000 + 100 + 20 + 7 \] --- ### Writing in Short Form Convert each expanded form expression into its standard numerical form. 1. **First Expression:** \[ 3 \times 10^{5} + 4 \times 10^{5} + 6 \times 10^{4} + 9 \times 10^{3} + 8 \times 10^{2} + 2 \times 10^{1} + 7 \] **Calculation:** \[ 300,\!000 + 400,\!000 + 60,\!000 + 9,\!000 + 800 + 20 + 7 = 769,\!827 \] **Short Form:** \[ 769,\!827 \] 2. **Second Expression:** \[ 8 \times 10^{7} + 4 \times 10^{5} + 2 \times 10^{4} + 6 \times 10^{2} + 7 \times 10^{1} + 3 \] **Calculation:** \[ 80,\!000,\!000 + 400,\!000 + 20,\!000 + 600 + 70 + 3 = 80,\!420,\!673 \] **Short Form:** \[ 80,\!420,\!673 \] 3. **Third Expression:** \[ 4 \times 10^{5} + 6 \times 10^{1} + 7 \times 10^{8} + 3 \times 10^{2} + 5 \times 10^{6} + 8 \times 10^{4} \] **Calculation:** \[ 700,\!000,\!000 + 5,\!000,\!000 + 400,\!000 + 80,\!000 + 300 + 60 = 705,\!480,\!360 \] **Short Form:** \[ 705,\!480,\!360 \] --- ### Summary - **a)** \( 3 \times 10^{5} = 300,\!000 \) - **b)** \( 7 \times 10^{5} = 700,\!000 \) - **c)** \( 5 \times 10^{7} = 50,\!000,\!000 \) - **d)** \( 8 \times 10^{6} = 8,\!000,\!000 \) - **Expanded Form of 9,432,127:** \[ 9 \times 10^{6} + 4 \times 10^{5} + 3 \times 10^{4} + 2 \times 10^{3} + 1 \times 10^{2} + 2 \times 10^{1} + 7 \times 10^{0} \] - **Short Forms:** 1. \( 769,\!827 \) 2. \( 80,\!420,\!673 \) 3. \( 705,\!480,\!360 \) Feel free to ask if you need further explanations or assistance!