Question

11 which correctly compares the values of the digits 2 and 6 in the number 243,695? a $2 \times 100 < 6 \times 100$ b $2 \times 1,000 > 6 \times 100$ c $2 \times 10,000 > 6 \times 100$ d $2 \times 100,000 > 6 \times 100$

Explanation:

First, we identify the place values of 2 and 6 in the number 243,6957 (assuming it's a typo and should be 243,695 or 243695). Let's assume the number is 243695.

• The digit 2 is in the hundred - thousands place, so its value is \(2\times100000\) (since \(100000 = 10\times10000=10\times10\times1000 = \cdots\), and \(100000=10^{5}\)).
• The digit 6 is in the hundreds place, so its value is \(6\times100\) (since \(100 = 10^{2}\)).

Now we calculate the values:

• Value of 2: \(2\times100000 = 200000\)
• Value of 6: \(6\times100=600\)

Now we check each option:

Step 1: Analyze Option A

\(2\times100 = 200\), \(6\times100 = 600\). Since \(200<600\), this is incorrect because the value of 2 is much larger than 200.

Step 2: Analyze Option B

\(2\times1000 = 2000\), \(6\times100 = 600\). Since \(2000>600\), but the value of 2 is \(2\times100000\) not \(2\times1000\), so this is incorrect.

Step 3: Analyze Option C

\(2\times10000 = 20000\), \(6\times100 = 600\). Since \(20000>600\), but the value of 2 is \(2\times100000\) not \(2\times10000\), so this is incorrect.

Step 4: Analyze Option D

\(2\times100000=200000\), \(6\times100 = 600\). Since \(200000>600\), this is correct.

Answer:

D. \(2\times100,000>6\times100\)