Introducing Decimals
Read place value to the right of the decimal point, convert between fractions and decimals, and compare decimals digit by digit.
1 What decimals are
Decimals are another way to write fractions with denominators 10, 100, 1000 — using place value instead of a fraction bar.
Places to the right
In 5.28: the 2 is in the tenths place (worth 0.2), the 8 is in the hundredths place (worth 0.08). Each step right is ten times smaller.
Fraction ↔ decimal
34 = 0.75: say “three fourths,” then write it as 75 hundredths. 0.6 = 610 = 35: say “six tenths,” then simplify.
Compare digit by digit
Line up the decimal points and compare left to right: 0.6 vs 0.59 — the tenths are 6 vs 5, so 0.6 > 0.59. Longer is not bigger: 0.59 has more digits but is smaller than 0.6.
Money is decimals
$3.25 = 3 dollars and 25 cents: the digits after the point are hundredths of a dollar.
2 See it: place value in 5.28
Every digit has a place — and a value.
3 Worked examples
Read the places, convert both ways, compare digit by digit.
- Thinking: the 2 sits in the first place after the point: the tenths.
- One tenth is 0.1, so two tenths are 0.2.
- The 2 is worth 0.2.
- Thinking: line up the points and compare the tenths: 6 vs 5.
- 6 > 5, so 0.6 > 0.59.
- More digits does not mean bigger!
- Thinking: rename 3/4 as hundredths: 3/4 = 75/100.
- 75 hundredths = 0.75.
- So 3/4 = 0.75.
- Thinking: 0.35 = 35 hundredths = 35/100.
- Simplify: divide by 5 → 7/20.
- So 0.35 = 7/20.
4 Common mistakes
Two traps catch almost everyone.
5 Key vocabulary
- Tenths
- The first place after the decimal point (0.1).
- Hundredths
- The second place after the decimal point (0.01).
- Thousandths
- The third place after the decimal point (0.001).
- Terminating decimal
- A decimal that ends, like 0.75.
- Place value
- What a digit is worth based on its position.
6 Quick check
Try these, then reveal the answers.
Key points to remember
- Places after the point: tenths, hundredths, thousandths — each ten times smaller.
- Fractions with denominator 10/100/1000 translate directly to decimals.
- Compare decimals digit by digit from the left; longer is not bigger.
- 0.6 = 0.60: trailing zeros do not change the value.
- Money is decimals: $3.25 = 3 dollars and 25 hundredths.