What Is A Decimal? Place Value, Fractions And Examples

The short version

A decimal is a number written with a decimal point, where the digits to the right of the point stand for parts of a whole: tenths, hundredths, thousandths and so on.
0.7 means 7 tenths (7/10). 0.07 means 7 hundredths (7/100). Each place to the right is worth one tenth of the place before it.
More digits doesn’t mean bigger. 0.5 is larger than 0.45, because 5 tenths beats 4 tenths.
Every decimal can be written as a fraction, and every fraction can be written as a decimal by dividing the top by the bottom.

What is a decimal? It’s a way to write a number that includes a part of a whole, using a dot called the decimal point. Digits to the left of the point are whole numbers. Digits to the right are fractions with 10, 100, 1,000 and so on as the bottom number. In 3.25, the 3 is three wholes and the .25 is 25 hundredths, so 3.25 is the same as 3 and 25/100.

Money is the example most kids already know: $4.75 is 4 whole dollars and 75 hundredths of a dollar, which is 75 cents. Decimals work the same way for measurements, sports times, prices and anything else that doesn’t come out to a whole number.

What is a decimal made of? Place value

Decimals are built on the same place value system as whole numbers, just extended past the ones place. Moving one place right divides the value by 10. Moving one place left multiplies it by 10.

Here’s 52.708 broken apart:

Digit	Place	Value	As a fraction
5	Tens	50	50
2	Ones	2	2
7	Tenths	0.7	7/10
0	Hundredths	0	0/100
8	Thousandths	0.008	8/1000

Two things stand out. There’s no “oneths” place: the first spot after the point is tenths. And the place names mirror the whole-number side (tens and tenths, hundreds and hundredths), centered on the ones place. That near-symmetry is where kids tend to get mixed up.

How to read a decimal out loud

Say the whole number, say “and” for the decimal point, read the digits after the point as a normal number, then name the last place.

52.708 is “fifty-two and seven hundred eight thousandths.”
0.35 is “thirty-five hundredths.”
6.4 is “six and four tenths.”

In everyday talk people say “six point four,” which is fine. Saying it the long way helps kids hear that 6.4 means 6 and 4/10.

What are decimals used for?

Money: $12.99 is 12 dollars and 99 hundredths of a dollar.
Measurement: a pencil might be 17.5 cm long, a baby might weigh 7.2 lb.
Time and sports: a 100 meter dash might take 12.84 seconds.
Grades and averages: a GPA of 3.6, or a batting average of .275.
Science: body temperature of 98.6 degrees Fahrenheit.

Decimals and fractions are two ways to write the same thing

A decimal is a fraction whose bottom number is 10, 100, 1,000 or another power of 10. That makes converting easy in one direction and only a little harder in the other.

Decimal to fraction

Write the digits over the place value of the last digit, then simplify.
0.6 = 6/10 = 3/5
0.25 = 25/100 = 1/4
0.125 = 125/1000 = 1/8

Fraction to decimal

Divide the numerator by the denominator.
3/4 = 3 ÷ 4 = 0.75
5/8 = 5 ÷ 8 = 0.625
1/3 = 1 ÷ 3 = 0.333…, where the 3 repeats forever

Fraction	Decimal	Fraction	Decimal
1/2	0.5	1/10	0.1
1/4	0.25	1/5	0.2
3/4	0.75	1/8	0.125
1/3	0.333…	2/3	0.666…

A decimal that stops, like 0.625, is called a terminating decimal. One that repeats a pattern forever, like 0.333…, is a repeating decimal, usually written with a bar over the part that repeats.

Comparing and ordering decimals

Line the numbers up by their decimal points and compare place by place, starting from the left. The first place where the digits differ decides it. If one number runs out of digits, add zeros so they’re the same length; that doesn’t change the value.

Worked example: which is bigger, 0.5 or 0.45?

Write them with the same number of places: 0.50 and 0.45.
Ones: both 0. Tenths: 5 vs 4. Stop there.
0.5 is bigger.

As fractions, that’s 50/100 against 45/100. Once both are written to the same length, the extra digit in 0.45 stops looking like an advantage.

Worked example: order 2.3, 2.03, 2.33 and 2.303 from least to greatest

Pad to three places: 2.300, 2.030, 2.330, 2.303.
Compare as if they were 2300, 2030, 2330 and 2303.
Least to greatest: 2.03, 2.3, 2.303, 2.33

Common mistakes with decimals

“Longer is bigger.” A kid who thinks 0.125 is bigger than 0.5 is treating the digits after the point like a whole number. This is the most common decimal misconception by far.
“Shorter is bigger.” Some kids overcorrect and decide 0.3 must beat 0.35 because tenths are bigger than hundredths. Padding with zeros (0.30 vs 0.35) fixes both errors.
Dropping a zero placeholder. “Four and six hundredths” is 4.06, not 4.6.
Misreading the places. Calling the first place after the point “ones” or “tens” instead of tenths.
Lining up the right edge when adding. For 3.5 + 1.25, the decimal points have to line up, not the last digits. The answer is 4.75.

Practice problems

What is the value of the 6 in 3.462?
Write “twelve and nine hundredths” as a decimal.
Which is greater: 0.7 or 0.68?
Write 0.35 as a fraction in simplest form.
Write 3/8 as a decimal.
Order from least to greatest: 0.4, 0.38, 0.405, 0.04
Round 4.768 to the nearest tenth.
Write 2/3 as a decimal.

Answers

6 hundredths, or 0.06.
12.09
0.7 (compare 0.70 and 0.68: 7 tenths beats 6 tenths).
35/100 = 7/20
3 ÷ 8 = 0.375
0.04, 0.38, 0.4, 0.405
4.8 (the hundredths digit is 6, so round the 7 up).
0.666…, written with a bar over the 6, or about 0.67.

If your kid is stuck on decimals

When decimals don’t make sense, the gap is almost always one of two older skills: whole-number place value or fractions. A kid who isn’t sure that the 4 in 340 means 4 tens will have no way to reason about tenths and hundredths. A kid who doesn’t really get that 7/10 means 7 of 10 equal parts will memorize decimal rules without understanding them, and those rules fall apart on the first tricky problem.

If your child asks “what is a decimal, really?”, that’s a good sign. They want to know what the digits mean. A quick check at home: ask your child which is bigger, 0.3 or 0.25, and why. The “why” matters more than the answer. Decimals normally show up in fourth grade and get heavy use in fifth, which you can see in math skills by grade level. Shaky decimals and fractions also tend to resurface years later, as we explain in why algebra trouble usually starts with fourth grade fractions. And if you’re not sure whether this is a small bump or a pattern, these 12 signs by grade level can help.

Frequently asked questions

What are decimals in math, in simple words?

Decimals are numbers with a point in them. The point splits the whole number part from the part that’s less than one. 2.5 means two and a half.

Is 0.5 the same as 1/2?

Yes. 0.5 is 5 tenths, which is 5/10, and 5/10 simplifies to 1/2.

Is a whole number a decimal?

Any whole number can be written as a decimal by adding a point and zeros: 7 = 7.0 = 7.00. Usually, though, “decimal” means a number with digits after the point.

What is a decimal point?

It’s the dot that separates the ones place from the tenths place. Everything to its left is at least one whole; everything to its right is a part of a whole.

What grade do kids learn decimals?

Kids usually meet tenths and hundredths in fourth grade, often through money and fractions with 10 or 100 on the bottom. Fifth grade adds thousandths and all four operations, and sixth grade builds fluency.

Find the actual gap

If decimals aren’t clicking, it’s worth finding out whether the real issue is place value, fractions or something before that. Math Anon begins with a short adaptive assessment that pinpoints the missing skills and gives you a written report on what it found.

After that, your child works on those specific skills for about 20 minutes a day, and you get a weekly progress report so you can see it moving. The assessment is $49, credited back in full on your first month. Here’s our pricing, or you can start the assessment now.

What Is A Decimal? Place Value, Fractions And Examples

The short version