Question

the value of the 2 in 204.75 is how many times the value of the 2 in 103.52? 10 times 100 times 1,000 times 10,000 times

Explanation:

Step1: Identify place values

In 204.75, the 2 is in the hundreds place, so its value is \(2\times100 = 200\). In 103.52, the 2 is in the hundredths place, so its value is \(2\times\frac{1}{100}=0.02\).

Step2: Calculate the ratio

Divide the value of 2 in 204.75 by the value of 2 in 103.52: \(\frac{200}{0.02}=\frac{200}{\frac{2}{100}} = 200\times\frac{100}{2}=10000\)? Wait, no, wait. Wait, 200 divided by 0.02: 0.02 times 10000 is 200? Wait, no, 0.02 times 1000 is 20, 0.02 times 10000 is 200. Wait, no, let's recalculate. 200 divided by 0.02: multiply numerator and denominator by 100 to eliminate decimals: \(\frac{200\times100}{0.02\times100}=\frac{20000}{2} = 10000\)? Wait, no, that's wrong. Wait, 2 in 204.75 is 200 (hundreds place: \(2\times10^2\)), 2 in 103.52 is 0.02 (hundredths place: \(2\times10^{-2}\)). The ratio is \(10^2 / 10^{-2}=10^{4}=10000\)? Wait, no, \(10^2\) divided by \(10^{-2}\) is \(10^{2 - (-2)}=10^4 = 10000\). Wait, but that can't be. Wait, no, wait 204.75: the 2 is in the hundreds place (200), 103.52: the 2 is in the hundredths place (0.02). So 200 / 0.02 = 10000? Wait, no, 0.02 times 10000 is 200. Yes. Wait, but the options have 10, 100, 1000, 10000. Wait, but maybe I made a mistake in place value. Wait, 204.75: digits are 2 (hundreds), 0 (tens), 4 (ones), 7 (tenths), 5 (hundredths). So 2 is 200. 103.52: 1 (hundreds), 0 (tens), 3 (ones), 5 (tenths), 2 (hundredths). So 2 is 0.02. Then 200 / 0.02 = 10000. So the answer is 10,000 times. Wait, but let me check again. Wait, 200 divided by 0.02: 0.02 * 10000 = 200. Yes. So the ratio is 10000.

Answer:

10,000 times