Lesson 3: Decimals

1⃣ What Is a Decimal?

A decimal is a special type of fraction. Instead of writing numbers over a denominator (like ½ or 3/4), decimals use a decimal point (.) to separate whole numbers from fractional parts.

🔹 Real-Life Example:

• Money is often written in decimal form:

• $1.00 = one whole dollar

• $0.10 = ten cents (or 10/100)

• $0.25 = twenty-five cents (or 25/100)

How to Read Decimals

Decimals are read based on place values:

• 0.1 is read as “one-tenth” (1/10)

• 0.01 is read as “one-hundredth” (1/100)

• 0.001 is read as “one-thousandth” (1/1000)

📌 Key Concept: The farther a number is from the decimal point, the smaller its value.

2⃣ Understanding Place Values

Numbers to the left of the decimal point represent whole numbers.

Numbers to the right of the decimal point represent fractional parts.

Place Value Chart:

Hundreds Tens Ones Decimal Point Tenths Hundredths Thousandths

3 6 2 . 1 4 7

🔹 Example Breakdown (362.147):

• Hundreds place: 3 → (300)

• Tens place: 6 → (60)

• Ones place: 2 → (2)

• Tenths place: 1 → (1/10 or 0.1)

• Hundredths place: 4 → (4/100 or 0.04)

• Thousandths place: 7 → (7/1000 or 0.007)

📌 Key Concept: Whole numbers get bigger as they move left. Decimal numbers get smaller as they move right.

3⃣ Converting Between Fractions and Decimals

✔ Fractions to Decimals:

• 1/10 = 0.1

• 3/100 = 0.03

• 7/1000 = 0.007

✔ Decimals to Fractions:

• 0.2 = 2/10

• 0.45 = 45/100

• 0.005 = 5/1000

📌 Key Concept: The denominator of a decimal fraction is always 10, 100, 1000, etc.

4⃣ Adding and Subtracting Decimals

✔ Step 1: Line Up the Decimal Points

• Just like with whole numbers, decimals must be written in columns where digits of the same place value are directly above or below each other.

✔ Step 2: Add or Subtract Normally

• Start from the rightmost digits, just like with whole numbers.

• Keep the decimal point in the same place in the final answer.

🔹 Example (Addition):

  12.3

+  4.56

---------

  16.86

• The decimal points are lined up.

• Add column by column.

🔹 Example (Subtraction):

  10.75

-  3.6

---------

   7.15

• Line up decimal points.

• Add a 0 (10.75 - 3.60) to make digits even.

📌 Key Concept: Always align decimal points when adding or subtracting.

5⃣ Using a Calculator for Decimals

For some exams, a calculator is allowed. Learning to use one correctly will save time.

✔ Calculator Tips:

• Always enter numbers exactly as they appear.

• Use the decimal point button (.) when entering decimal values.

• Double-check that numbers are lined up correctly before hitting =.

📌 GED, HiSET, and TASC Test Calculator Information:

• GED & TASC use the Texas Instruments TI-30XS.

• HiSET: Provides a calculator at the test center (handheld or on-screen).

• Some TASC sections do not allow a calculator.

6⃣ Test-Taking Tip: Learn to Use a Calculator!

✔ Practice with simple decimal sums before your test.

✔ If using an on-screen calculator, make sure you know how to enter numbers properly.

✔ If taking a paper-based test, familiarize yourself with the TI-30XS calculator.

📌 Lesson Recap

✔ A decimal is a fraction written with a decimal point.

✔ Place value determines how big or small a number is.

✔ Fractions and decimals can be converted into each other.

✔ To add or subtract decimals, always line up the decimal points.

✔ Calculators can be helpful, but learning to do calculations manually is also important.