The place value of a digit at the hundredths place is \(\tfrac{1}{10}\) times the same digit at the tenths place.
Why this is true (step by step):
In decimals, each place to the right is \(\tfrac{1}{10}\) of the place to its left.
Tenths place value: \(\tfrac{1}{10}\)
Hundredths place value: \(\tfrac{1}{100}\)
Let the digit be \(d\). If \(d\) is in the tenths place, its value is:
\(d \times \tfrac{1}{10}\)
If the same \(d\) is in the hundredths place, its value is:
\(d \times \tfrac{1}{100}\)
Compare the two values by making a ratio (hundredths ÷ tenths):
\(\dfrac{d \times \tfrac{1}{100}}{d \times \tfrac{1}{10}}\)
Cancel \(d\): \(\dfrac{\tfrac{1}{100}}{\tfrac{1}{10}}\)
Compute: \(\tfrac{1}{100} \div \tfrac{1}{10} = \tfrac{1}{10}\)
Example: take \(d=5\).
Tenths: \(0.5 = 5 \times \tfrac{1}{10}\)
Hundredths: \(0.05 = 5 \times \tfrac{1}{100}\)
\(0.05\) is \(\tfrac{1}{10}\) of \(0.5\).
Conclusion: The hundredths value is \(\tfrac{1}{10}\) of the tenths value, so the statement is true.