3 P3: Decimals
Working with Decimals
Introduction
Decimals represent parts of a whole using powers of ten. Procedural fluency with decimals means being able to read, write, and perform arithmetic operations (add, subtract, multiply, divide) with understanding and accuracy.
For pre-service teachers, mastering these skills ensures they can model place value reasoning, align decimal points correctly, and explain results clearly to students.
Reading and Writing Decimals
Decimals are read by naming the whole number, then reading the decimal part as a fraction.
Reading Examples
| Decimal | How to Read |
|---|---|
| 0.46 | forty-six hundredths |
| 0.058 | fifty-eight thousandths |
| 76.83 | seventy-six and eighty-three hundredths |
| 888.71 | eight hundred eighty-eight and seventy-one hundredths |
| 39.52 | thirty-nine and fifty-two hundredths |
Writing Examples
| Words | Decimal |
|---|---|
| forty-six hundredths | 0.46 |
| fifty-eight thousandths | 0.058 |
| seventy-six and eighty-three hundredths | 76.83 |
| three hundred fifty and three hundredths | 350.03 |
| two thousandths | 0.002 |
Adding and Subtracting Decimals
To add or subtract decimals, line up the decimal points so digits of equal place value are in the same column. Then perform the operation as with whole numbers.
Steps
- Align decimal points.
- Add or subtract digits.
- Bring the decimal point straight down.
Example 1 — Addition
[latex]5.794 + 2.475 = 8.269[/latex]
Example 2 — Subtraction
[latex]16.91 - 9.623 = 7.287[/latex]
Tip: If necessary, add zeros so both numbers have the same number of decimal places.
Multiplying Decimals
When multiplying decimals, ignore the decimal points and multiply as whole numbers. Then count the total number of decimal places in both factors and place the decimal that many places from the right in the product.
Example 3
[latex]3.42 \times 2.03 = 6.9426[/latex]
Count 4 decimal places total → [latex]6.9426[/latex] → round as needed.
Example 4
[latex]4.3 \times 0.06 = 0.258[/latex]
Dividing Decimals
When dividing by a decimal, move the decimal point in both divisor and dividend until the divisor becomes a whole number. Then divide as usual.
Example 5
[latex]6.4 \div 0.2 = 32[/latex]
Move decimal one place right in both → [latex]64 \div 2 = 32[/latex]
Example 6
[latex]4.4 - 0.098 = 4.302[/latex]
Place Value Review
Each position to the right of the decimal point represents a fraction with a denominator that is a power of ten:
| Place | Fraction Value | Example |
|---|---|---|
| tenths | [latex]\dfrac{1}{10}[/latex] | 0.3 = three-tenths |
| hundredths | [latex]\dfrac{1}{100}[/latex] | 0.46 = forty-six hundredths |
| thousandths | [latex]\dfrac{1}{1000}[/latex] | 0.058 = fifty-eight thousandths |
Understanding this structure helps students correctly name, compare, and compute with decimals.
Common Student Errors and Corrections
| Error | Example | Correction Strategy |
|---|---|---|
| Misaligning decimal points | 5.4 + 0.78 = 6.118 | Use graph paper or placeholders to align correctly. |
| Forgetting zeros when subtracting | 16.9 − 9.623 | Add trailing zeros: 16.900 − 9.623. |
| Counting decimal places incorrectly when multiplying | 0.6 × 0.4 = 0.24 (ok), but many write 2.4 | Count total decimal places in both factors. |
| Ignoring place value when dividing | 0.8 ÷ 0.02 = 0.4 | Move decimals so divisor is a whole number. |
H5P Practice Activities
H5P 1: Reading and Writing Decimals
Prompt: Type the decimal that matches each word phrase.
H5P Placeholder:
Examples
- Forty-six hundredths →
0.46 - Fifty-eight thousandths →
0.058 - Seventy-six and eighty-three hundredths →
76.83
H5P 2: Fill-in-the-Blank — Decimal to Words
Prompt: Write each decimal in words.
H5P Placeholder:
Examples
- 39.52 →
thirty-nine and fifty-two hundredths - 0.065 →
sixty-five thousandths - 0.002 →
two thousandths
H5P 3: Fill-in-the-Blank — Add and Subtract
Prompt: Perform each operation and type your answer.
H5P Placeholder:
Examples
- [latex]5.794 + 2.475[/latex] →
8.269 - [latex]16.91 - 9.623[/latex] →
7.287 - [latex]11.272 - 8.6[/latex] →
2.672
H5P 4: Fill-in-the-Blank — Multiply and Divide
Prompt: Perform each operation.
H5P Placeholder:
Examples
- [latex]6.4 \div 0.2[/latex] →
32 - [latex]4.3 \times 0.06[/latex] →
0.258 - [latex]3.2 \times 2.45[/latex] →
7.84
H5P 5: Word Problems — Applying Decimal Operations
Prompt: Solve each word problem and round answers to the nearest hundredth.
H5P Placeholder:
- A rope is 5.6 m long. A piece 2.47 m long is cut off. How long is the remaining piece? →
3.13 m - A pencil costs $0.48 and an eraser costs $0.35. What is the total cost of 3 pencils and 2 erasers?
Solution: latex+(2\times0.35)=1.44+0.70=2.14[/latex] →\$2.14 - A runner completed 4 laps of 0.75 km each. How many kilometers total? →
3.00 km
Reflection for Pre-Service Teachers
- Why is aligning decimal points critical for accuracy in addition and subtraction?
- How can place value charts or base-ten blocks help explain decimal operations?
- What patterns do students often miss when multiplying or dividing by powers of ten?
- How can rounding errors affect interpretation of real-world problems?
Summary
Procedural fluency with decimals develops from:
- Understanding place value.
- Practicing accurate alignment and computation.
- Converting between word and numeric form.
- Applying reasonableness checks using estimation.
Mastery of these procedures allows pre-service teachers to confidently model and explain decimal operations in elementary classrooms.