Question

What expression is equivalent to 304,672 in expanded form using powers of ten?

Options:

Option 1: 3 × 100,000 + 4 × 10,000 + 6 × 1,000 + 7 × 100 + 2 × 10

Option 2: 3 × 100,000 + 0 × 10,000 + 4 × 1,000 + 6 × 100 + 7 × 10 + 2 × 1

Option 3: 30 × 10,000 + 4 × 1,000 + 6 × 100 + 7 × 10 + 2 × 1

Option 4: 3 × 100,000 + 0 × 10,000 + 4 × 1,000 + 0 × 100 + 6 × 10 + 7 × 1 + 2 × 0

Answer 1

The expression equivalent to 304,672 in expanded form using powers of ten is Option 2: 3 × 100,000 + 0 × 10,000 + 4 × 1,000 + 6 × 100 + 7 × 10 + 2 × 1.

Step-by-step explanation:

The expression equivalent to 304,672 in expanded form using powers of ten is the one that breaks down each digit according to its place value. We can do this by multiplying each digit by a power of 10 that corresponds to its position in the number. The power of ten increases by a power of 1 with each move to the left in a standard number. Starting with the unit position (100), the next position to the left is the tens (101), then hundreds (102), and so on. Therefore, the tens place is 10 times the value of the units, the hundreds place is 100 times the value of the units, and so on.

Using this information, we can see that the correct option for expressing 304,672 in expanded form is:

Option 2: 3 × 100,000 + 0 × 10,000 + 4 × 1,000 + 6 × 100 + 7 × 10 + 2 × 1.

This equals:

3 × 105 + 0 × 104 + 4 × 103 + 6 × 102 + 7 × 101 + 2 × 100.