What is the expanded form of 31,476.52?(1 point)

Question

Responses

(3×10,000)+(1×1,000)+(4×100)+(7×10)+(6×1)+(5×1100)+(2×11,000)
open paren 3 times 10 comma 000 close paren plus open paren 1 times 1 comma 000 close paren plus open paren 4 times 100 close paren plus open paren 7 times 10 close paren plus open paren 6 times 1 close paren plus open paren 5 times 1 over 100 close paren plus open paren 2 times the fraction with numerator 1 and denominator 1 comma 000 close paren

(3×10,000)+(1×1,000)+(4×100)+(6×10)+(7×1)+(5×110)+(2×1100)
open paren 3 times 10 comma 000 close paren plus open paren 1 times 1 comma 000 close paren plus open paren 4 times 100 close paren plus open paren 6 times 10 close paren plus open paren 7 times 1 close paren plus open paren 5 times 1 tenth close paren plus open paren 2 times 1 over 100 close paren

(3×10,000)+(1×1,000)+(4×100)+(7×10)+(6×1)+(5×110)+(2×1100)
open paren 3 times 10 comma 000 close paren plus open paren 1 times 1 comma 000 close paren plus open paren 4 times 100 close paren plus open paren 7 times 10 close paren plus open paren 6 times 1 close paren plus open paren 5 times 1 tenth close paren plus open paren 2 times 1 over 100 close paren

(3×10,000)+(1×1,000)+(4×100)+(6×10)+(7×1)+(5×1100)+(2×11,000)

Answer 1

The correct expanded form of 31,476.52 is:

\[ (3 \times 10,000) + (1 \times 1,000) + (4 \times 100) + (7 \times 10) + (6 \times 1) + (5 \times \frac{1}{10}) + (2 \times \frac{1}{100}) \]

This is equivalent to:

• \(3 \times 10,000\) for the ten-thousands place,
• \(1 \times 1,000\) for the thousands place,
• \(4 \times 100\) for the hundreds place,
• \(7 \times 10\) for the tens place,
• \(6 \times 1\) for the units place,
• \(5 \times \frac{1}{10}\) for the tenths place,
• \(2 \times \frac{1}{100}\) for the hundredths place.

However, let’s review the options provided in your question to find the closest match:

The first option correctly lays out the components of the number but contains an error in interpreting \(5\) and \(2\):

• \(5\) should correspond to \(5 \times \frac{1}{10}\) (for the tenths place),
• \(2\) should correspond to \(2 \times \frac{1}{100}\) (for the hundredths place).

Thus, the closest option to the correct expanded form is:

(3×10,000)+(1×1,000)+(4×100)+(7×10)+(6×1)+(5×(1/10))+(2×(1/100))

If we compare that with the options, the first one is the EASIEST to understand, also flagging to ensure you have to convert decimals appropriately for further calculations as provided.