What is a decimal point in math?
A decimal point is the dot that separates the whole-number part of a number from its fractional part. Digits to its left are ones, tens and hundreds; digits to its right are tenths, hundredths and thousandths. In 46.25 the point sits between 6 ones and 2 tenths, and you read it aloud as “and”.
Decimal Point in a picture
Formal definition and notation
In base-ten notation, the decimal point marks the position between the ones place (100) and the tenths place (10−1). A digit k places to the left of the point is multiplied by 10k−1, and a digit k places to the right is multiplied by 110k. A whole number has an unwritten decimal point after its ones digit: 8 = 8.0.
| Symbol | Read it as | Meaning |
|---|---|---|
| . | point, or "and" in number names | the US decimal point: 2.5 is “two and five tenths”, often said “two point five” |
| , | comma | many countries use a decimal comma instead (2,5); in the US the comma separates thousands (2,500) |
| 0.6 | zero point six | a leading zero before the point makes it easy to see; .6 and 0.6 are the same number |
Key facts
- Each place to the left of the point is 10 times the place to its right; each place to the right is one tenth of the place to its left.
- Read the point as “and”: 305.07 is “three hundred five and seven hundredths“. Do not say “and” anywhere else in a number.
- Zeros at the end of the fractional part do not change the value: 4.5 = 4.50 = 4.500.
- To add or subtract decimals, line up the decimal points so tenths sit under tenths.
- Multiplying or dividing by 10, 100 or 1,000 moves the point, not the digits’ order.
Moving the decimal point
- n
- the number of zeros in 10, 100, 1,000, … (the exponent of 10)
- right
- the number gets bigger
- left
- the number gets smaller
Fill empty places with zeros: 0.4 × 1,000 = 400 and 5 ÷ 1,000 = 0.005.
Try it: digits around the point
Change any digit with the arrows. Watch how its value depends on which side of the decimal point it sits, and how far away.
Decimal Point examples, step by step
Example 1: Writing a decimal from words
Write “seven and nine hundredths” as a decimal.
- “Seven” is the whole-number part, and “and” marks the decimal point: 7.
- Hundredths is the 2nd place after the point, so 9 goes there with a 0 in the tenths place.
Answer: Seven and nine hundredths is 7.09.
Example 2: Multiplying by a power of 10
Find 0.38 × 1,000.
- 1,000 has 3 zeros, so move the point 3 places to the right.
- 0.38 → 3.8 → 38. → 380. (fill the empty place with 0).
Answer: 0.38 × 1,000 = 380.
Example 3: Lining up decimal points
A hiker walks 12.5 km, then 3.75 km, then 0.6 km. How far does she walk in all?
- Write each number with the decimal points in one column: 12.50, 3.75, 0.60.
- Add the hundredths: 0 + 5 + 0 = 5. Add the tenths: 5 + 7 + 6 = 18, write 8 and regroup 1 one.
- Add the ones and tens: 2 + 3 + 0 + 1 = 6, and 1 ten.
- Put the point straight below the others: 16.85.
Answer: She walks 16.85 km.
Common mistakes
Lining up points keeps tenths with tenths and ones with ones; lining up the right edge mixes place values.
A whole number’s decimal point is just after its ones digit, even when it is not written.
In math, “and” tells the listener where the decimal point goes, so using it elsewhere changes the number.
Dividing by 10 makes a number smaller, so the point must move left.
Not to be confused with
A decimal is the whole number written with a point, like 3.14; the decimal point is only the dot inside it.
In the US a comma groups digits by thousands (12,500) and the point separates parts of one (12.5). 12,500 is a thousand times 12.5.
A raised dot means multiply: 3 · 4 = 12. A decimal point sits on the line: 3.4 is three and four tenths.
Quick check: 3 questions
In 528.67, which digit is just to the right of the decimal point?
Answer: B. The point sits between 8 (ones) and 6 (tenths), so 6 is just to its right. 8 is just to the left, 7 is in the hundredths place, and 2 is in the tens place.Show answer and explanation
What is 4.06 × 100?
Answer: A. Multiplying by 100 moves the point 2 places right: 4.06 → 406. 40.6 moves only 1 place, 4.0600 just adds zeros (same value), and 4,060 moves 3 places.Show answer and explanation
Which is the correct sum of 9 + 0.45?
Answer: C. Write 9 as 9.00 and line up the points: 9.00 + 0.45 = 9.45. 0.54 adds 9 to the hundredths place, 9.045 puts the digits one place too far right, and 94.5 ignores the point.Show answer and explanation
Decimal Point: frequently asked questions
Why do we say "and" for the decimal point?
“And” tells the listener where the whole-number part ends and the fractional part begins. 3.08 is “three and eight hundredths”. That is why careful readers do not use “and” inside whole numbers: “two hundred and five” could be heard as 200.005 instead of 205. In everyday speech many people say “point” instead: “three point zero eight”.
Does every number have a decimal point?
Yes, in a sense. A whole number has a decimal point right after its ones digit, but we usually leave it out because nothing follows it: 25 is the same as 25.0 or 25.00. You need to write it when you line up 25 with a decimal like 3.75 to add or subtract.
Why do some countries use a comma instead of a decimal point?
Both marks are accepted, and different countries adopted different customs. Much of Europe and Latin America writes three and a half as 3,5, while the US, the UK and many others write 3.5. Spaces are often used to group thousands in those countries, as in 12 500, so the comma is free for the decimal.
Practice and tools
Sources
- Common Core State Standards, Grade 4 Number and Operations: Fractions (4.NF.C.6)
- Common Core State Standards, Grade 5 Number and Operations in Base Ten (5.NBT.A.2, 5.NBT.A.3.a)
- OpenStax, Prealgebra 2e, 5.1 Decimals
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 4.NF.C.6, CCSS 5.NBT.A.2, CCSS 5.NBT.A.3.a
Cite this entry
Effortless Math Team. “Decimal Point.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/decimal-point/
Flashcard
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