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Write in 7,921.995 in expanded form.(1 point)

Responses

(7×1,000)+(9×100)+(2×10)+(1×1)+(9×110)+(2×1100)+(1×11,000)
open paren 7 times 1 comma 000 close paren plus open paren 9 times 100 close paren plus open paren 2 times 10 close paren plus open paren 1 times 1 close paren plus open paren 9 times 1 tenth close paren plus open paren 2 times 1 over 100 close paren plus open paren 1 times the fraction with numerator 1 and denominator 1 comma 000 close paren - no response given

(7×1,000)+(9×100)+(2×10)+(1×1)+(9×110)+(9×1100)+(5×11,000)
open paren 7 times 1 comma 000 close paren plus open paren 9 times 100 close paren plus open paren 2 times 10 close paren plus open paren 1 times 1 close paren plus open paren 9 times 1 tenth close paren plus open paren 9 times 1 over 100 close paren plus open paren 5 times the fraction with numerator 1 and denominator 1 comma 000 close paren - no response given

(7×1,000,000)+(9×100,000)+(2×10,000)+(1×1,000)+(9×100)+(9×10)+(5×1)
open paren 7 times 1 comma 000 comma 000 close paren plus open paren 9 times 100 comma 000 close paren plus open paren 2 times 10 comma 000 close paren plus open paren 1 times 1 comma 000 close paren plus open paren 9 times 100 close paren plus open paren 9 times 10 close paren plus open paren 5 times 1 close paren - incorrect

(7×1,000)+(9×100)+(2×10)+(1×1)+(9×0)+(9×110)+(5×1100)

1 answer

To write the number 7,921.995 in expanded form, we break it down by place value for both the whole number part (7,921) and the decimal part (0.995).

  1. Whole Number Part (7,921):

    • 7 is in the thousands place: \(7 \times 1000 = 7000\)
    • 9 is in the hundreds place: \(9 \times 100 = 900\)
    • 2 is in the tens place: \(2 \times 10 = 20\)
    • 1 is in the ones place: \(1 \times 1 = 1\)

  2. Decimal Part (0.995):

    • 9 is in the tenths place: \(9 \times \frac{1}{10} = 0.9\)
    • 9 is in the hundredths place: \(9 \times \frac{1}{100} = 0.09\)
    • 5 is in the thousandths place: \(5 \times \frac{1}{1000} = 0.005\)

Putting it all together, we have: \[ (7 \times 1000) + (9 \times 100) + (2 \times 10) + (1 \times 1) + (9 \times \frac{1}{10}) + (9 \times \frac{1}{100}) + (5 \times \frac{1}{1000}) \]

In a cleaner format: \[ (7 \times 1000) + (9 \times 100) + (2 \times 10) + (1 \times 1) + (9 \times \frac{1}{10}) + (9 \times \frac{1}{100}) + (5 \times \frac{1}{1000}) \]

Therefore, the correct expanded form for 7,921.995 is: \[ (7 \times 1000) + (9 \times 100) + (2 \times 10) + (1 \times 1) + (9 \times \frac{1}{10}) + (9 \times \frac{1}{100}) + (5 \times \frac{1}{1000}) \]