Introduction to Decimals

Concept Explanation

Decimals are a way of writing numbers that aren’t whole numbers. They use a decimal point to separate the whole number part from the fractional part. The digits to the right of the decimal point represent tenths, hundredths, thousandths, and so on.

For example, in the decimal 3.45:

• 3 is in the ones place
• 4 is in the tenths place (4/10)
• 5 is in the hundredths place (5/100)

So 3.45 = 3 + 4/10 + 5/100 = 3 + 0.4 + 0.05 = 3.45

Worked Examples

Example 1

Problem: Write 0.7 as a fraction.
Solution: $\frac{7}{10}$
Explanation: The 7 is in the tenths place, so it represents 7 tenths.

Example 2

Problem: Write $\frac{3}{4}$ as a decimal.
Solution: 0.75
Explanation: Divide 3 by 4: 3 ÷ 4 = 0.75

Example 3

Problem: What is the value of the underlined digit in 5.2\underline84?
Solution: 8 hundredths or $\frac{8}{100}$
Explanation: The digit 8 is in the hundredths place.

Common Errors

Practice Problems

1. Problem: Write 0.35 as a fraction.
   Solution:

   $\frac{35} {100} = \frac{7} {20}$

2. Problem:

   Write $\frac{1} {5}$ as a decimal.

   Solution: 0.2
3. Problem: What is the value of the underlined digit in 12.3\underline45?
   Solution:

   4 hundredths or $\frac{4} {100}$

4. Problem:

   Write $\frac{3} {8}$ as a decimal.

   Solution: 0.375
5. Problem: Order from least to greatest: 0.7, 0.07, 0.77
   Solution: 0.07, 0.7, 0.77

Real-World Application Example

Decimals are used in money (dollars and cents), measurements (meters and centimeters), and many scientific calculations. Understanding decimals helps with everyday tasks like shopping (comparing prices), cooking (measuring ingredients), and sports (tracking statistics like batting averages).