Fractions and Decimals - Introduction to Decimals (Tenths and Hundredths)

A decimal is a way of writing a fraction whose denominator is a power of ten, such as $10$, $100$, or $1000$. It represents a part of a whole number using a decimal point to separate the whole number part from the fractional part.

The Decimal Point is a dot used to separate the whole number from the fractional part. To the left of the point are the Ones, Tens, and Hundreds; to the right are the Tenths and Hundredths. Visualizing a place value chart, it looks like: [Hundreds] [Tens] [Ones] . [Tenths] [Hundredths].

Tenths represent one part out of ten equal parts of a whole. If you imagine a long rectangular bar divided into $10$ equal vertical strips, shading one strip represents $\frac{1}{10}$ or $0.1$. Ten tenths make one whole: $10 \times 0.1 = 1.0$.

Hundredths represent one part out of one hundred equal parts of a whole. Imagine a large square grid divided into $10 \times 10$ smaller squares (totaling $100$ squares). Shading just one tiny square represents $\frac{1}{100}$ or $0.01$. One hundred hundredths make one whole: $100 \times 0.01 = 1.0$.

The relationship between Tenths and Hundredths is that one tenth is equal to ten hundredths ($0.1 = 0.10$). Visually, if you look at a hundredths grid, one full column of $10$ small squares is exactly the same size as one bar in a tenths grid.

Decimals can be written as fractions and vice versa. For example, the fraction $\frac{7}{10}$ is written as $0.7$ in decimal form, and the fraction $\frac{24}{100}$ is written as $0.24$. When writing hundredths, the second digit after the decimal point is the hundredths place.

Placeholders are used when a decimal has no value in a specific position. For example, '3 ones and 5 hundredths' is written as $3.05$. The $0$ in the tenths place is a placeholder to show there are zero tenths.