To represent the number three hundred two thousand and fifty-seven in expanded form, we must break it down into its components according to their place values. Let's take a step-by-step approach to understand this.
1. Identify each digit and its place value:
- The number given is 302,057.
- Break it down into individual place values:
- 3 is in the hundred thousand's place,
- 0 is in the ten thousand's place,
- 2 is in the thousand's place,
- 0 is in the hundred's place,
- 5 is in the ten's place,
- 7 is in the one's place.
2. Write each digit with its corresponding place value:
- 3 in the hundred thousand's place: [tex]\( 300,000 \)[/tex]
- 2 in the thousand's place: [tex]\( 2,000 \)[/tex]
- 5 in the ten's place: [tex]\( 50 \)[/tex]
- 7 in the one's place: [tex]\( 7 \)[/tex]
3. Combine these values to form the expanded form:
- [tex]\( 300,000 + 2,000 + 50 + 7 \)[/tex]
Now, let's compare these values with the options provided:
a) [tex]\( 300,000 + 2,000 + 50 + 7 \)[/tex]
b) [tex]\( 302,000 + 57 \)[/tex]
c) [tex]\( 302 + 1,000 + 50 + 7 \)[/tex]
d) [tex]\( 300 + 2,000 + 50 + 7 \)[/tex]
The correct expanded form of 302,057 is given in option (a):
[tex]\[ 300,000 + 2,000 + 50 + 7 \][/tex]
So, the correct answer is:
[tex]\[ 300,000 + 2,000 + 50 + 7 \][/tex]
