Question
What is the expanded form of 23.75?(1 point)%0D%0AResponses%0D%0A%0D%0A(2×10)+(3×1)+(7×110)+(5×1100)%0D%0Aleft parenthesis 2 times 10 right parenthesis plus left parenthesis 3 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 100 End Fraction right parenthesis%0D%0A%0D%0A(2×10)+(3×1)+(5×110)+(7×1100)%0D%0Aleft parenthesis 2 times 10 right parenthesis plus left parenthesis 3 times 1 right parenthesis plus left parenthesis 5 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 7 times Start Fraction 1 over 100 End Fraction right parenthesis%0D%0A%0D%0A(2×10)+(3×1)+(7×1101)+(5×1102)%0D%0Aleft parenthesis 2 times 10 right parenthesis plus left parenthesis 3 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 superscript 1 baseline End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 10 squared End Fraction right parenthesis%0D%0A%0D%0A(5×10)+(7×1)+(3×110)+(2×1100)
Write the expanded form of 357.25(1 point)%0D%0AResponses%0D%0A%0D%0A(3×100)+(5×10)+(7×1)+(2×110)+(5×11,000)%0D%0Aleft parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 2 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 1,000 End Fraction right parenthesis%0D%0A%0D%0A(3×100)+(5×10)+(7×1)+(2×1100)%0D%0Aleft parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 2 times Start Fraction 1 over 100 End Fraction right parenthesis%0D%0A%0D%0A(3×100)+(5×10)+(7×1)+(2×110)+(5×1100)%0D%0Aleft parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 2 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 100 End Fraction right parenthesis%0D%0A%0D%0A(3×100)+(5×10)+(7×1)+(5×110)+(2×1100)
What is the expanded form of 8,471.716?(1 point)%0D%0AResponses%0D%0A%0D%0A(8×103)+(4×102)+(7×101)+(1×100)+(7×1101)+(1×1102)+(6×1103) %0D%0Aleft parenthesis 8 times 10 cubed right parenthesis plus left parenthesis 4 times 10 squared right parenthesis plus left parenthesis 7 times 10 superscript 1 baseline right parenthesis plus left parenthesis 1 times 10 superscript 0 baseline right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 superscript 1 baseline End Fraction right parenthesis plus left parenthesis 1 times Start Fraction 1 over 10 squared End Fraction right parenthesis plus left parenthesis 6 times Start Fraction 1 over 10 cubed End Fraction right parenthesis%0D%0A%0D%0A(8×1,000)+(4×100)+(7×10)+(1×1)+(7×11)+(1×110)+(6×1100) %0D%0Aleft parenthesis 8 times 1,000 right parenthesis plus left parenthesis 4 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 1 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 1 End Fraction right parenthesis plus left parenthesis 1 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 6 times Start Fraction 1 over 100 End Fraction right parenthesis%0D%0A%0D%0A(8×1,000)+(4×100)+(7×10)+(1×1)+(7×110)+(1×1100)%0D%0Aleft parenthesis 8 times 1,000 right parenthesis plus left parenthesis 4 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 1 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 1 times Start Fraction 1 over 100 End Fraction right parenthesis%0D%0A%0D%0A(8×1,000)+(4×100)+(7×10)+(1×1)+(7×110)+(1×1100)+(6×11,000)
Write the expanded form of 357.25(1 point)%0D%0AResponses%0D%0A%0D%0A(3×100)+(5×10)+(7×1)+(2×110)+(5×11,000)%0D%0Aleft parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 2 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 1,000 End Fraction right parenthesis%0D%0A%0D%0A(3×100)+(5×10)+(7×1)+(2×1100)%0D%0Aleft parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 2 times Start Fraction 1 over 100 End Fraction right parenthesis%0D%0A%0D%0A(3×100)+(5×10)+(7×1)+(2×110)+(5×1100)%0D%0Aleft parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 2 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 100 End Fraction right parenthesis%0D%0A%0D%0A(3×100)+(5×10)+(7×1)+(5×110)+(2×1100)
What is the expanded form of 8,471.716?(1 point)%0D%0AResponses%0D%0A%0D%0A(8×103)+(4×102)+(7×101)+(1×100)+(7×1101)+(1×1102)+(6×1103) %0D%0Aleft parenthesis 8 times 10 cubed right parenthesis plus left parenthesis 4 times 10 squared right parenthesis plus left parenthesis 7 times 10 superscript 1 baseline right parenthesis plus left parenthesis 1 times 10 superscript 0 baseline right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 superscript 1 baseline End Fraction right parenthesis plus left parenthesis 1 times Start Fraction 1 over 10 squared End Fraction right parenthesis plus left parenthesis 6 times Start Fraction 1 over 10 cubed End Fraction right parenthesis%0D%0A%0D%0A(8×1,000)+(4×100)+(7×10)+(1×1)+(7×11)+(1×110)+(6×1100) %0D%0Aleft parenthesis 8 times 1,000 right parenthesis plus left parenthesis 4 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 1 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 1 End Fraction right parenthesis plus left parenthesis 1 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 6 times Start Fraction 1 over 100 End Fraction right parenthesis%0D%0A%0D%0A(8×1,000)+(4×100)+(7×10)+(1×1)+(7×110)+(1×1100)%0D%0Aleft parenthesis 8 times 1,000 right parenthesis plus left parenthesis 4 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 1 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 1 times Start Fraction 1 over 100 End Fraction right parenthesis%0D%0A%0D%0A(8×1,000)+(4×100)+(7×10)+(1×1)+(7×110)+(1×1100)+(6×11,000)
Answers
Answered by
GPT-4o mini
Let's break down the expanded forms requested for each number step by step.
### 1. Expanded Form of 23.75
The expanded form of a decimal number separates each digit based on its place value (units, tenths, hundredths, etc.).
For 23.75:
- **2** is in the tens place: \( 2 \times 10 \)
- **3** is in the ones place: \( 3 \times 1 \)
- **7** is in the tenths place: \( 7 \times \frac{1}{10} \)
- **5** is in the hundredths place: \( 5 \times \frac{1}{100} \)
Thus, the correct expanded form is:
\[
(2 \times 10) + (3 \times 1) + (7 \times \frac{1}{10}) + (5 \times \frac{1}{100})
\]
### 2. Expanded Form of 357.25
Following the same logic for 357.25:
- **3** is in the hundreds place: \( 3 \times 100 \)
- **5** is in the tens place: \( 5 \times 10 \)
- **7** is in the ones place: \( 7 \times 1 \)
- **2** is in the tenths place: \( 2 \times \frac{1}{10} \)
- **5** is in the hundredths place: \( 5 \times \frac{1}{100} \)
The correct expanded form for this number is:
\[
(3 \times 100) + (5 \times 10) + (7 \times 1) + (2 \times \frac{1}{10}) + (5 \times \frac{1}{100})
\]
### 3. Expanded Form of 8,471.716
For the number 8,471.716:
- **8** is in the thousands place: \( 8 \times 1000 \)
- **4** is in the hundreds place: \( 4 \times 100 \)
- **7** is in the tens place: \( 7 \times 10 \)
- **1** is in the ones place: \( 1 \times 1 \)
- **7** is in the tenths place: \( 7 \times \frac{1}{10} \)
- **1** is in the hundredths place: \( 1 \times \frac{1}{100} \)
- **6** is in the thousandths place: \( 6 \times \frac{1}{1000} \)
The correct expanded form for this number is:
\[
(8 \times 1000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000})
\]
This means the expanded forms for your questions are as follows:
- **23.75**: \( (2 \times 10) + (3 \times 1) + (7 \times \frac{1}{10}) + (5 \times \frac{1}{100}) \)
- **357.25**: \( (3 \times 100) + (5 \times 10) + (7 \times 1) + (2 \times \frac{1}{10}) + (5 \times \frac{1}{100}) \)
- **8,471.716**: \( (8 \times 1000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000}) \)
### 1. Expanded Form of 23.75
The expanded form of a decimal number separates each digit based on its place value (units, tenths, hundredths, etc.).
For 23.75:
- **2** is in the tens place: \( 2 \times 10 \)
- **3** is in the ones place: \( 3 \times 1 \)
- **7** is in the tenths place: \( 7 \times \frac{1}{10} \)
- **5** is in the hundredths place: \( 5 \times \frac{1}{100} \)
Thus, the correct expanded form is:
\[
(2 \times 10) + (3 \times 1) + (7 \times \frac{1}{10}) + (5 \times \frac{1}{100})
\]
### 2. Expanded Form of 357.25
Following the same logic for 357.25:
- **3** is in the hundreds place: \( 3 \times 100 \)
- **5** is in the tens place: \( 5 \times 10 \)
- **7** is in the ones place: \( 7 \times 1 \)
- **2** is in the tenths place: \( 2 \times \frac{1}{10} \)
- **5** is in the hundredths place: \( 5 \times \frac{1}{100} \)
The correct expanded form for this number is:
\[
(3 \times 100) + (5 \times 10) + (7 \times 1) + (2 \times \frac{1}{10}) + (5 \times \frac{1}{100})
\]
### 3. Expanded Form of 8,471.716
For the number 8,471.716:
- **8** is in the thousands place: \( 8 \times 1000 \)
- **4** is in the hundreds place: \( 4 \times 100 \)
- **7** is in the tens place: \( 7 \times 10 \)
- **1** is in the ones place: \( 1 \times 1 \)
- **7** is in the tenths place: \( 7 \times \frac{1}{10} \)
- **1** is in the hundredths place: \( 1 \times \frac{1}{100} \)
- **6** is in the thousandths place: \( 6 \times \frac{1}{1000} \)
The correct expanded form for this number is:
\[
(8 \times 1000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000})
\]
This means the expanded forms for your questions are as follows:
- **23.75**: \( (2 \times 10) + (3 \times 1) + (7 \times \frac{1}{10}) + (5 \times \frac{1}{100}) \)
- **357.25**: \( (3 \times 100) + (5 \times 10) + (7 \times 1) + (2 \times \frac{1}{10}) + (5 \times \frac{1}{100}) \)
- **8,471.716**: \( (8 \times 1000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000}) \)
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