Question
What is the expanded form of 8,471.716?
(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
(8×103)+(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)
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
(8×103)+(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
Answers
Answered by
GPT-4o mini
To find the expanded form of the number 8,471.716, we will break it down into its constituent parts, by considering the place value of each digit.
The number 8,471.716 can be expanded as follows:
- The digit **8** is in the thousands place: \( 8 \times 1,000 \)
- The digit **4** is in the hundreds place: \( 4 \times 100 \)
- The digit **7** is in the tens place: \( 7 \times 10 \)
- The digit **1** is in the ones place: \( 1 \times 1 \)
- The digit **7** after the decimal point is in the tenths place: \( 7 \times \frac{1}{10} \)
- The digit **1** is in the hundredths place: \( 1 \times \frac{1}{100} \)
- The digit **6** is in the thousandths place: \( 6 \times \frac{1}{1,000} \)
Putting this all together, the expanded form of 8,471.716 is:
\[
(8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000})
\]
Thus, the most accurate expression from your options is:
\[
(8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000})
\]
You have presented two similar options:
1. \( (8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000}) \)
2. \( (8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times 11) + (1 \times 110) + (6 \times 1,100) \)
From the first option you're providing, the correct expanded form is:
\[
(8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000})
\]
This option captures the correct place values after decimal points.
The number 8,471.716 can be expanded as follows:
- The digit **8** is in the thousands place: \( 8 \times 1,000 \)
- The digit **4** is in the hundreds place: \( 4 \times 100 \)
- The digit **7** is in the tens place: \( 7 \times 10 \)
- The digit **1** is in the ones place: \( 1 \times 1 \)
- The digit **7** after the decimal point is in the tenths place: \( 7 \times \frac{1}{10} \)
- The digit **1** is in the hundredths place: \( 1 \times \frac{1}{100} \)
- The digit **6** is in the thousandths place: \( 6 \times \frac{1}{1,000} \)
Putting this all together, the expanded form of 8,471.716 is:
\[
(8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000})
\]
Thus, the most accurate expression from your options is:
\[
(8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000})
\]
You have presented two similar options:
1. \( (8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000}) \)
2. \( (8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times 11) + (1 \times 110) + (6 \times 1,100) \)
From the first option you're providing, the correct expanded form is:
\[
(8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000})
\]
This option captures the correct place values after decimal points.