Introduction to Decimals
What Is This?
A decimal is a way of writing numbers that are between whole numbers — or more precisely, a way of showing parts of a whole using a dot called the decimal point. The number 0.7 means seven tenths. The number 3.25 means three wholes, two tenths, and five hundredths. Decimals are everywhere: prices, measurements, sports scores, and science all use them.
Why Does It Matter?
Decimals are a natural extension of the place value system you already know. Once you understand decimals, you can work with money (dollars and cents), measure length in centimeters and millimeters, read a thermometer, and compare test scores. Decimals and fractions are two different ways of writing the same values — mastering decimals connects everything you have learned about fractions to the real world.
The Decimal Point
The decimal point is the dot that separates the whole number part (on the left) from the fractional part (on the right).
3 . 2 5
↑ ↑ ↑
ones tenths hundredths
Reading left to right, each position to the right of the decimal point is ten times smaller than the one before it.
Place Value Chart
| Hundreds | Tens | Ones | · | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|
| 100 | 10 | 1 | · | 1/10 | 1/100 | 1/1000 |
Example: 47.36
| Tens | Ones | · | Tenths | Hundredths |
|---|---|---|---|---|
| 4 | 7 | · | 3 | 6 |
- 4 is in the tens place → value = 40
- 7 is in the ones place → value = 7
- 3 is in the tenths place → value = 3/10
- 6 is in the hundredths place → value = 6/100
Read aloud: "forty-seven and thirty-six hundredths"
Tenths
When you divide a whole into 10 equal parts, each part is one tenth, written as 0.1 or 1/10.
Example: A chocolate bar is split into 10 equal pieces. You eat 3 pieces.
- Fraction: 3/10
- Decimal: 0.3
- Read as: "three tenths"
| Decimal | Fraction | Picture |
|---|---|---|
| 0.1 | 1/10 | 1 out of 10 equal parts |
| 0.4 | 4/10 | 4 out of 10 equal parts |
| 0.9 | 9/10 | 9 out of 10 equal parts |
Hundredths
When you divide a whole into 100 equal parts, each part is one hundredth, written as 0.01 or 1/100.
Think of a 10×10 grid of 100 squares. Each small square is 0.01.
Example: You colour 37 squares out of 100.
- Fraction: 37/100
- Decimal: 0.37
- Read as: "thirty-seven hundredths"
| Decimal | Fraction | Meaning |
|---|---|---|
| 0.01 | 1/100 | 1 out of 100 parts |
| 0.25 | 25/100 | 25 out of 100 parts |
| 0.75 | 75/100 | 75 out of 100 parts |
Reading and Writing Decimals
How to Read a Decimal
- Read the whole number part (left of the decimal point)
- Say "and" for the decimal point
- Read the digits to the right as a whole number
- Say the place value name of the last digit
Examples:
| Decimal | How to Read It |
|---|---|
| 0.6 | "six tenths" |
| 2.4 | "two and four tenths" |
| 0.38 | "thirty-eight hundredths" |
| 5.07 | "five and seven hundredths" |
| 12.45 | "twelve and forty-five hundredths" |
Decimals on a Number Line
A number line helps you see where decimals sit between whole numbers.
Tenths between 0 and 1:
0 --- 0.1 --- 0.2 --- 0.3 --- 0.4 --- 0.5 --- 0.6 --- 0.7 --- 0.8 --- 0.9 --- 1.0
Hundredths between 0.3 and 0.4:
0.30 - 0.31 - 0.32 - 0.33 - 0.34 - 0.35 - 0.36 - 0.37 - 0.38 - 0.39 - 0.40
Decimals and Fractions — The Connection
Decimals and fractions are two ways of writing the same value. The denominator tells you which decimal place to use.
| Fraction | Denominator | Decimal |
|---|---|---|
| 3/10 | 10 → tenths | 0.3 |
| 7/10 | 10 → tenths | 0.7 |
| 9/100 | 100 → hundredths | 0.09 |
| 43/100 | 100 → hundredths | 0.43 |
| 1/2 | → 5/10 | 0.5 |
| 1/4 | → 25/100 | 0.25 |
| 3/4 | → 75/100 | 0.75 |
Converting a Fraction to a Decimal
Method 1 — Denominator is already 10 or 100: Write the numerator in the correct decimal place.
- 7/10 → 0.7
- 53/100 → 0.53
Method 2 — Convert the denominator to 10 or 100:
- 1/2 → multiply top and bottom by 5 → 5/10 → 0.5
- 3/4 → multiply top and bottom by 25 → 75/100 → 0.75
- 1/5 → multiply top and bottom by 2 → 2/10 → 0.2
Method 3 — Divide numerator by denominator:
- 3/4 → 3 ÷ 4 = 0.75
- 1/2 → 1 ÷ 2 = 0.5
Zeros in Decimals — Be Careful!
Leading zeros
0.5 means five tenths. The zero before the decimal point just shows there is no whole number — it does not change the value.
Placeholder zeros
0.05 and 0.5 are not the same.
- 0.5 = 5/10 = 50/100
- 0.05 = 5/100
The zero between the decimal point and the 5 is a placeholder — it pushes the 5 into the hundredths place.
Trailing zeros (after the last digit)
0.5 = 0.50 = 0.500 — these are all equal. Adding zeros to the right of the last decimal digit does not change the value. This is useful when comparing or adding decimals.
Worked Examples
Worked Example 1: Write 0.6 as a fraction in simplest form.
- 0.6 = 6/10
- GCF of 6 and 10 is 2
- 6/10 ÷ 2/2 = 3/5
Worked Example 2: What is the value of the digit 4 in 7.842?
- The digits after the decimal: 8 (tenths), 4 (hundredths), 2 (thousandths)
- The digit 4 is in the hundredths place
- Its value is 4/100 = 0.04
Worked Example 3: Write 9/20 as a decimal.
- 9/20 — multiply top and bottom by 5 → 45/100
- 0.45
Worked Example 4: Place 0.4, 0.04, and 0.40 in order from least to greatest.
- 0.04 = 4/100
- 0.4 = 40/100
- 0.40 = 40/100
- Order: 0.04 < 0.4 = 0.40
Common Mistakes
Mistake 1: Thinking more digits = larger number 0.9 > 0.25 even though 0.25 has more digits. Always compare place by place — tenths first, then hundredths.
Mistake 2: Ignoring placeholder zeros 0.3 and 0.03 are very different. 0.3 = 30/100 while 0.03 = 3/100. The placeholder zero matters.
Mistake 3: Reading the decimal point as "point" and stopping "Five point three" is informal. The correct reading is "five and three tenths" — it tells you the actual place value.
Mistake 4: Dropping the zero before the decimal point Always write 0.7, not .7. The leading zero signals that there is no whole number and prevents misreading.
Key Takeaways
- A decimal uses a dot (decimal point) to separate the whole number from the fractional part
- The first place to the right of the decimal point is tenths (1/10); the second is hundredths (1/100)
- Decimals and fractions represent the same values — fractions with denominator 10 or 100 convert directly
- Placeholder zeros change the value (0.5 ≠ 0.05); trailing zeros do not (0.5 = 0.50)
- Read decimals by naming the whole part, saying "and," then reading the decimal digits followed by the last place value name
Practice and Resources
Ready to practise? Try our Grade 3-5 Introduction to Decimals Worksheet with problems covering place value, reading decimals, and fraction-decimal conversion. Test yourself with the Grade 3-5 Math Practice Test.