Question

Use decimal expansion to write 320.75 in expanded form.

(3×1,000)+(2×100)+(0×10)+(7×1)+(5×110)
(
3
×
1
,
000
)
+
(
2
×
100
)
+
(
0
×
10
)
+
(
7
×
1
)
+
(
5
×
1
10
)
open paren 3 times 1 comma 000 close paren plus open paren 2 times 100 close paren plus open paren 0 times 10 close paren plus open paren 7 times 1 close paren plus open paren 5 times 1 tenth close paren

(3×100)+(2×10)+(0×1)+(7×110)+(5×1100)
(
3
×
100
)
+
(
2
×
10
)
+
(
0
×
1
)
+
(
7
×
1
10
)
+
(
5
×
1
100
)
open paren 3 times 100 close paren plus open paren 2 times 10 close paren plus open paren 0 times 1 close paren plus open paren 7 times 1 tenth close paren plus open paren 5 times 1 over 100 close paren

(3×10)+(2×1)+(0×110)+(7×1100)+(5×11,000)
(
3
×
10
)
+
(
2
×
1
)
+
(
0
×
1
10
)
+
(
7
×
1
100
)
+
(
5
×
1
1
,
000
)
open paren 3 times 10 close paren plus open paren 2 times 1 close paren plus open paren 0 times 1 tenth close paren plus open paren 7 times 1 over 100 close paren plus open paren 5 times the fraction with numerator 1 and denominator 1 comma 000 close paren

(3×100)+(2×10)+(1×1)+(7×110)+(5×1100)

Answer 1

To express 320.75 in expanded form using decimal expansion, we can break it down by place value. The number can be separated into its constituent parts based on the value of each digit:

- The digit "3" is in the hundreds place, which is \(3 \times 100\).
- The digit "2" is in the tens place, which is \(2 \times 10\).
- The digit "0" is in the units place (ones), which is \(0 \times 1\).
- The digit "7" is in the tenths place, which is \(7 \times \frac{1}{10}\).
- The digit "5" is in the hundredths place, which is \(5 \times \frac{1}{100}\).

Putting this all together, the expanded form of 320.75 can be written as:

\[
(3 \times 100) + (2 \times 10) + (0 \times 1) + (7 \times \frac{1}{10}) + (5 \times \frac{1}{100})
\]

This fully represents the decimal number 320.75 in expanded form.