Question

a number has the same digit in its hundreds place and its hundredths place. how many times greater is the value of the digit in the hundreds place than the value of the digit in the hundredths place? 10,000 100 1,000 100,000

Explanation:

Step1: Recall place values

The hundreds place has a place value of \(100\) (since \(100 = 10^2\)), and the hundredths place has a place value of \(0.01\) (since \(0.01=\frac{1}{100}=10^{- 2}\)).

Step2: Calculate the ratio

Let the digit in both places be \(d\). The value of the digit in the hundreds place is \(d\times100\), and the value of the digit in the hundredths place is \(d\times0.01\). To find how many times greater the hundreds - place digit's value is, we calculate the ratio \(\frac{d\times100}{d\times0.01}\). The \(d\) terms cancel out, and we have \(\frac{100}{0.01}=\frac{100}{\frac{1}{100}} = 100\times100=10000\).

Answer:

10,000