Understanding Decimals Through Hundredths

Decimals are just another way to write fractions! When we divide a whole number into 10 or 100 equal parts, we can use decimals to show those parts easily.

The Decimal Place Value

In a decimal number, the decimal point separates the whole numbers from the fractional parts. The places to the right of the decimal point have specific names:

• Tenths place: The first digit after the decimal point. It shows how many pieces you have if the whole is divided into 10 equal parts.
• Hundredths place: The second digit after the decimal point. It shows how many pieces you have if the whole is divided into 100 equal parts.

For example, let's look at the number $3.62$:

• $3$ is the whole number.
• $6$ is in the tenths place (meaning $\frac{6}{10}$).
• $2$ is in the hundredths place (meaning $\frac{2}{100}$).

Connecting Decimals to Fractions

Decimals and fractions with denominators of $10$ or $100$ are closely connected. You can easily switch between them:

• Tenths: $\frac{8}{10}$ is written as $0.8$.
• Hundredths: $\frac{47}{100}$ is written as $0.47$.

If you have a fraction like $\frac{5}{100}$, you must put a zero in the tenths place to hold its value, showing there are no full tenths, only hundredths. This is written as $0.05$.

Example Problems

1. Write $\frac{47}{100}$ as a decimal. Because the denominator is $100$, the decimal will go to the second spot after the decimal point (the hundredths place). Answer: $0.47$

2. What is the value of the 6 in $3.62$? Look at the position of the $6$. It is the first digit after the decimal point, which is the tenths place. Answer: The value is $6$ tenths, which can be written as $0.6$ or $\frac{6}{10}$.

3. Write $0.8$ as a fraction. The $8$ is in the tenths place, which means we have $8$ parts out of a total of $10$. Answer: $\frac{8}{10}$