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What is the expanded form of 8,471.716?(1 point) Responses (8×103)+(4×102)+(7×101)+(1×100)+(7×1101)+(1×1102)+(6×1103) left pare...Question
What is the expanded form of 8,471.716?(1 point) Responses (8×103)+(4×102)+(7×101)+(1×100)+(7×1101)+(1×1102)+(6×1103) left 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 (8×1,000)+(4×100)+(7×10)+(1×1)+(7×110)+(1×1100)+(6×11,000) left 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 plus left parenthesis 6 times Start Fraction 1 over 1,000 End Fraction right parenthesis (8×1,000)+(4×100)+(7×10)+(1×1)+(7×11)+(1×110)+(6×1100) left 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 (8×1,000)+(4×100)+(7×10)+(1×1)+(7×110)+(1×1100) left 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
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Answered by
GPT-4o mini
To express the number 8,471.716 in expanded form, we break it down into whole numbers and decimal parts based on the place value of each digit.
**Whole number part:**
- 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: \(1 \times 1\)
**Decimal part:**
- 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: \(6 \times \frac{1}{1000}\)
Now, putting it all together, the expanded form of 8,471.716 is:
\[
(8 \times 1000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000})
\]
So, the correct response from the options provided is:
**(8×1,000) + (4×100) + (7×10) + (1×1) + (7×\frac{1}{10}) + (1×\frac{1}{100}) + (6×\frac{1}{1000})**
**Whole number part:**
- 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: \(1 \times 1\)
**Decimal part:**
- 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: \(6 \times \frac{1}{1000}\)
Now, putting it all together, the expanded form of 8,471.716 is:
\[
(8 \times 1000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000})
\]
So, the correct response from the options provided is:
**(8×1,000) + (4×100) + (7×10) + (1×1) + (7×\frac{1}{10}) + (1×\frac{1}{100}) + (6×\frac{1}{1000})**
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