Question
What is the expanded form of 8,471.716?(1 point)
Responses
(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)+(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)+(7×110)+(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
(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
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Responses
(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)+(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)+(7×110)+(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
(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
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Answers
GPT-4o mini
To find the expanded form of the number 8,471.716, we break it down according to the place value of each digit:
- The digit 8 is in the thousands place, so it represents \(8 \times 1,000\).
- The digit 4 is in the hundreds place, so it represents \(4 \times 100\).
- The digit 7 is in the tens place, so it represents \(7 \times 10\).
- The digit 1 is in the ones place, so it represents \(1 \times 1\).
- The digit 7 in the tenths place (right of the decimal) represents \(7 \times \frac{1}{10}\) or \(7 \times 10^{-1}\).
- The digit 1 in the hundredths place represents \(1 \times \frac{1}{100}\) or \(1 \times 10^{-2}\).
- The digit 6 in the thousandths place represents \(6 \times \frac{1}{1000}\) or \(6 \times 10^{-3}\).
Putting this all together, the expanded form can be represented as:
\[
(8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000})
\]
Among the options given, this matches with:
\[
(8\times 1,000)+(4\times 100)+(7\times 10)+(1\times 1)+(7\times \frac{1}{10})+(1\times \frac{1}{100})+(6\times \frac{1}{1000})
\]
So, the correct response is:
**(8×1,000)+(4×100)+(7×10)+(1×1)+(7×\frac{1}{10})+(1×\frac{1}{100})+(6×\frac{1}{1000})**
- The digit 8 is in the thousands place, so it represents \(8 \times 1,000\).
- The digit 4 is in the hundreds place, so it represents \(4 \times 100\).
- The digit 7 is in the tens place, so it represents \(7 \times 10\).
- The digit 1 is in the ones place, so it represents \(1 \times 1\).
- The digit 7 in the tenths place (right of the decimal) represents \(7 \times \frac{1}{10}\) or \(7 \times 10^{-1}\).
- The digit 1 in the hundredths place represents \(1 \times \frac{1}{100}\) or \(1 \times 10^{-2}\).
- The digit 6 in the thousandths place represents \(6 \times \frac{1}{1000}\) or \(6 \times 10^{-3}\).
Putting this all together, the expanded form can be represented as:
\[
(8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000})
\]
Among the options given, this matches with:
\[
(8\times 1,000)+(4\times 100)+(7\times 10)+(1\times 1)+(7\times \frac{1}{10})+(1\times \frac{1}{100})+(6\times \frac{1}{1000})
\]
So, the correct response is:
**(8×1,000)+(4×100)+(7×10)+(1×1)+(7×\frac{1}{10})+(1×\frac{1}{100})+(6×\frac{1}{1000})**