How many times greater is a 7 in ten thousands place than a 7 in the hundreds place? Choose the number that is shown in expanded form: 700,000 + 20,000 + 80 + 3

Understand the Problem

The first question is asking how many times greater a digit in the ten-thousands place is compared to a digit in the hundreds place. The second question asks for the numerical value of an expression presented in expanded form.

Answer

1. $100$; 2. $720,083$

Steps to Solve

Identify Place Values

A digit in the ten-thousands place is worth $10,000$ times the digit, and a digit in the hundreds place is worth $100$ times the digit.

Calculate the Difference in Value

To determine how many times greater a $7$ in the ten-thousands place is compared to a $7$ in the hundreds place, compare their values:

Value of $7$ in ten-thousands place: $$ 7 \times 10,000 = 70,000 $$
Value of $7$ in hundreds place: $$ 7 \times 100 = 700 $$

Find the Ratio

To find how many times greater the ten-thousands place is than the hundreds place, divide the two values: $$ \frac{70,000}{700} = 100 $$

Evaluate the Expanded Form Expression

For the expression $700,000 + 20,000 + 80 + 3$, simply add the values:

$700,000 + 20,000 + 80 + 3 = 720,083$

The answer is $100$.
For the expanded form, the answer is $720,083$ (option C).

More Information

The ten-thousands place is 100 times greater than the hundreds place. The expanded form $700,000 + 20,000 + 80 + 3$ corresponds to the numerical value $720,083$.

Tips

Confusing the place values can lead to incorrect calculations. Ensure you understand that ten-thousands is $10,000$ and hundreds is $100$.
When calculating the expanded form, forget to include all components, which could lead to an incorrect total.

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