A decimal is a number written with a decimal point to show parts of a whole. Decimals use place value to represent tenths, hundredths, thousandths and more: in 3.14, the 1 means 1 tenth and the 4 means 4 hundredths. So 0.75 = 75100, and 0.5 is one half.
Digits after the decimal point count tenths, hundredths and thousandths. A hundred grid makes hundredths visible: 0.75 covers 75 of the 100 squares.
Formal definition and notation
A decimal writes a number in base ten with a decimal point separating the whole-number part from the fractional part. Each digit to the right of the point stands for a fraction whose denominator is a power of ten: tenths110, hundredths1100, thousandths 11000. Every rational number has a decimal form that either terminates, like 38 = 0.375, or repeats, like 23 = 0.666….
Symbol
Read it as
Meaning
0.75
seventy-five hundredths (or zero point seven five)
75100; the name comes from the last place used
0.3
zero point three repeating
the bar means the 3 repeats forever: 13
2.50
two and fifty hundredths
the same value as 2.5; zeros at the right end do not change a decimal
Key facts
Each place is worth one tenth of the place to its left: 1 tenth = 10 hundredths.
Line up decimal points before adding or subtracting decimals.
To compare decimals, line them up and compare place by place from the left: 0.5 = 0.50 is greater than 0.45.
To change a fraction to a decimal, divide the numerator by the denominator: 38 = 3 ÷ 8 = 0.375.
Multiplying by 10 moves the decimal point one place right; dividing by 10 moves it one place left.
Decimal place values
Decimal place values
0.375 = 310 + 7100 + 51000 = 3751000
tenths
first place right of the point
hundredths
second place right of the point
thousandths
third place right of the point
To write a decimal as a fraction, put the digits over 10, 100 or 1000 to match the last place, then simplify: 0.375 = 3751000 = 38.
Try it: build a decimal
Interactive
Raise or lower any digit, or select a digit to see its value. Places to the right of the decimal point are tenths, hundredths and thousandths.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
A fraction can have any denominator, like 27. A decimal always uses tenths, hundredths and other powers of ten, though any fraction can be rewritten as a decimal: 27 = 0.285714.
A percent is hundredths written with %: 0.75 = 75%. Move the decimal point two places right to change a decimal to a percent.
Quick check: 3 questions
Question 1 of 3
Which fraction equals 0.25?
Show answer and explanation
Answer: C.0.25 = 25100 = 14. Choice A puts 25 in the denominator, choice B uses tenths instead of hundredths (that is 2.5), and 25 = 0.4.
Question 2 of 3
Which number is greatest?
Show answer and explanation
Answer: A. Compare tenths first: 0.7, 0.65 and 0.699 have 7, 6 and 6 tenths, so 0.7 wins. 0.699 has the most digits but is still less than 0.700, and 0.07 has 0 tenths.
Question 3 of 3
What is 4.2 + 0.35?
Show answer and explanation
Answer: B. Line up the points: 4.20 + 0.35 = 4.55. Choices C and D add the digits as if they were whole numbers and then guess where the point goes, and choice A adds 0.35 to 4.02.
Decimal: frequently asked questions
How do you read a decimal out loud?
Read the whole number, say ‘and’ for the decimal point, then read the digits after the point as a whole number followed by the name of the last place. So 3.14 is ‘three and fourteen hundredths’ and 0.007 is ‘seven thousandths’. In everyday speech people also say ‘three point one four’.
How do you convert a decimal to a percent?
Multiply by 100, which moves the decimal point two places to the right, and add the percent sign. So 0.75 = 75%, 0.4 = 40% and 1.25 = 125%. To go back, divide by 100: 8% = 0.08. This works because percent means ‘per hundred’, and the second decimal place is hundredths.
What is a repeating decimal?
A repeating decimal has a digit or group of digits that repeats forever, marked with a bar: 13 = 0.3 and 111 = 0.09. It happens when the fraction’s simplified denominator has a prime factor other than 2 or 5. Fractions like 38 or 720 give terminating decimals instead.
NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Decimal PointA 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”.Number System · Grade 4, Grade 5, Grade 6DenominatorThe denominator is the bottom number in a fraction. It tells how many equal parts make one whole: in 35, the 5 means the whole is cut into 5 equal parts, and the numerator 3 counts the parts you have. 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It is also called lowest terms.Number System · Grade 4, Grade 5, Grade 6SimplifySimplify means to rewrite a number or expression in a shorter, easier form without changing its value. To simplify a fraction, divide the numerator and denominator by a common factor until none is left: 1824 = 34. To simplify an expression, combine like terms and do the operations you can: 3x + 2x = 5x.Number System · Grade 4, Grade 5, Grade 6RemainderA remainder is the amount left over when one whole number does not divide another evenly. In 23 ÷ 5, four groups of 5 make 20 and 3 are left, so 23 ÷ 5 = 4 R 3. The remainder is always smaller than the divisor. A remainder of 0 means the division is exact.Operations · Grade 4, Grade 5, Grade 6FractionA fraction is a number that names equal parts of a whole, written ab. The bottom number, the denominator, tells how many equal parts make one whole; the top number, the numerator, tells how many of those parts you have. So 34 means 3 of 4 equal parts. 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