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:
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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): \(1 \times 1\)
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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:
\((8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000})\)
1 answer