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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...Asked by realperson
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)+(7×11)+(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 (8×1,000)+(4×100)+(7×10)+(1×1)+(7×110)+(1×1100)+(6×11,000)
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Answered by
GPT-4o mini
The expanded form of the number 8,471.716 can be expressed as the sum of each digit multiplied by its respective place value. Here's how it breaks down:
- The digits to the left of the decimal point are 8, 4, 7, and 1:
- 8 is in the thousands place (10^3): \(8 \times 1,000\)
- 4 is in the hundreds place (10^2): \(4 \times 100\)
- 7 is in the tens place (10^1): \(7 \times 10\)
- 1 is in the ones place (10^0): \(1 \times 1\)
- The digits to the right of the decimal point are 7, 1, and 6:
- 7 is in the tenths place (10^-1): \(7 \times \frac{1}{10}\)
- 1 is in the hundredths place (10^-2): \(1 \times \frac{1}{100}\)
- 6 is in the thousandths place (10^-3): \(6 \times \frac{1}{1000}\)
Putting it all together, the expanded form is:
\[
(8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000})
\]
So, the correct choice from your options is:
\((8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000})\)
- The digits to the left of the decimal point are 8, 4, 7, and 1:
- 8 is in the thousands place (10^3): \(8 \times 1,000\)
- 4 is in the hundreds place (10^2): \(4 \times 100\)
- 7 is in the tens place (10^1): \(7 \times 10\)
- 1 is in the ones place (10^0): \(1 \times 1\)
- The digits to the right of the decimal point are 7, 1, and 6:
- 7 is in the tenths place (10^-1): \(7 \times \frac{1}{10}\)
- 1 is in the hundredths place (10^-2): \(1 \times \frac{1}{100}\)
- 6 is in the thousandths place (10^-3): \(6 \times \frac{1}{1000}\)
Putting it all together, the expanded form is:
\[
(8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000})
\]
So, the correct choice from your options is:
\((8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000})\)
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