Tenths and Hundredths - Comparing and Ordering Decimals

Understanding Tenths: A tenth represents one part out of ten equal parts of a whole. In decimal form, it is written as $0.1$ and as a fraction $\frac{1}{10}$. Visually, if you imagine a long rectangular bar divided into $10$ equal vertical strips, shading $1$ strip represents $0.1$.

Understanding Hundredths: A hundredth represents one part out of one hundred equal parts of a whole. It is written as $0.01$ or $\frac{1}{100}$. Visually, imagine a large square grid made of $100$ small identical squares ($10 \times 10$); shading just $1$ small square represents $0.01$.

Decimal Place Value: The decimal point separates the whole number from the fractional part. The first digit to the right of the decimal is the Tenths place, and the second digit is the Hundredths place. For example, in $4.56$, $4$ is the whole number, $5$ is in the tenths place, and $6$ is in the hundredths place.

Like and Unlike Decimals: Decimals having the same number of decimal places are called like decimals (e.g., $0.45$ and $0.12$). Decimals with different numbers of decimal places are unlike decimals (e.g., $0.5$ and $0.58$). To compare them easily, you can add a 'placeholder zero' to make them like decimals, such as changing $0.5$ to $0.50$.

Comparing Decimals: To compare two decimals, first compare the whole number parts. If they are equal, compare the tenths digits. If the tenths are also equal, compare the hundredths digits. For instance, $0.7$ is greater than $0.65$ because $0.7$ can be seen as $0.70$, and $70$ hundredths is more than $65$ hundredths.

Ordering Decimals: Ordering involves arranging decimals in Ascending Order (smallest to largest) or Descending Order (largest to smallest). Visually, this is like placing values on a number line where $0.01$ is very close to zero and $0.99$ is very close to $1$.