1/5 as a Decimal

One fifth is 0.2 and the division stops there

One fifth means one part out of five equal parts. Divide 1 by 5 and the answer is 0.2. There is no remainder, so the decimal ends after a single digit. Nothing repeats and nothing needs rounding.

Read 0.2 out loud as two tenths. That is the same amount as one fifth, because two tenths and one fifth describe the same slice of a whole: 2/10 reduces to 1/5 once you divide the top and the bottom by 2.

The percent form follows from the decimal. Multiply 0.2 by 100 and you get 20, so 1/5 is 20 percent. A fifth of a dollar is 20 cents, which is the same statement in coins.

The rest of this page runs the division in long form, lists every fifth from 1/5 to 5/5, and covers the reading mistakes that turn 0.2 into 0.02 or into 2.

The long division, one step at a time

Long division makes the answer visible. Set up 1.0 divided by 5. Five does not fit into 1, so the whole part is 0 and the decimal point goes in. Bring down a zero to make 10. Five fits into 10 exactly twice, 5 x 2 = 10, and the remainder is 0. The quotient reads 0.2 and the work is finished.

The same three lines handle 2/5. Two divided by five gives 0 with a remainder of 2, so bring down a zero for 20, and five goes in four times with nothing left over. That gives 2/5 = 0.4. For 3/5 the working line is 30 divided by 5 = 6, so the answer is 0.6. For 4/5 it is 40 divided by 5 = 8, so the answer is 0.8. For 5/5 the whole part is 1 and no decimal point is needed.

The pattern is easy to keep in mind: each fifth adds two tenths. One fifth lands at 0.2, two fifths at 0.4, three fifths at 0.6, and four fifths at 0.8. The digits are the even numbers 2, 4, 6, and 8 sitting in the tenths place.

Run the same fraction through the calculator on this page and the result matches the working line above. With 1 in the numerator box and 5 in the denominator box it reports 0.2, 20%, the reduced fraction 1/5, and a type line stating that the decimal terminates after one digit. Change the numerator to 3 and the same machinery returns 0.6, which is the third row of the table below.

The working line for every fifth fits in one short table, because the remainder drops to zero on the first step each time.

Read across a row for the whole story: the division, the quotient, and no rounding anywhere in it. A fifth never needs an ellipsis.

Fifths line up on the tenths grid

Because 1/5 = 2/10, every fifth lands on a tenths mark. That is why a fifths table is short and why the decimals look familiar. The table below gives the fraction, the decimal, the percent, and the coin value of each fifth of a dollar.

The table also works backward. If a sale takes 40 percent off, the fraction removed is 2/5 and the decimal is 0.4, so a $75 item drops by $30 and costs $45. If a sale takes 20 percent off, the fraction is 1/5, and the same $75 item drops by $15 and costs $60.

A cash drawer makes the fifth visible. A dollar breaks into five parts of 20 cents, and 20 cents is two dimes, so a cashier handing over a fifth of a dollar passes two coins rather than one. Four quarters fill the same dollar, and a quarter is 25 cents, which stands a nickel above the 20 cent fifth. That nickel is 5 cents, and 5 cents is 5 percent of a dollar, a fifth of the 25 cent gap.

From 0.2 to 20 percent and back

Percent means per hundred, so a percent is a decimal multiplied by 100. 0.2 x 100 = 20, which is written 20%. Going the other way, divide the percent by 100: 20 / 100 = 0.2.

Two checks keep the conversion honest. First, 20% of 85 is 17, and 0.2 x 85 is also 17, so the two forms agree. Second, 20% of 250 is 50, and one fifth of 250 is 50 as well. When both routes give the same number, the conversion is right.

A common slip is to read 20% as 0.02. The decimal for 20% has one digit after the point, 0.2. The number 0.02 is 2 percent, and 0.002 is 0.2 percent. Each step to the right of the point divides by ten, and each step down in percent divides by ten as well.

One fifth of a bill, a price, or a down payment

Restaurant math uses fifths often, because a 20 percent tip is one fifth of the check. On a $64 check, 20% is $12.80 and the total comes to $76.80. On a $45 check the tip is $9.00. Splitting a $120 check five ways gives $24 each, which is the same as taking one fifth.

Mortgage and car math uses fifths too. A 20 percent down payment on a $315,000 house is $63,000, and the loan covers the other $252,000. On a $24,000 car, 20 percent down is $4,800.

Discounts run the same way in reverse. Twenty percent off $85 takes $17 off and leaves $68. A fifth off and 20 percent off describe the same discount, so the two phrases can be swapped at the register without changing the price.

The table lists one fifth of the amounts that come up most often, and each row can be checked by multiplying back: 48 x 5 = 240 returns the original amount.

The share line in the calculator reports the same figures. Set the amount box to 260 and it shows $52.00; set it to 1,100 and it shows $220.00. Saving one fifth of a $2,800 paycheck sets aside $560 a month, and 560 x 5 = 2,800 closes the loop. When an amount looks awkward, divide by ten and then double: one fifth of 340 is 68, because 34 x 2 = 68.

The same division turns up outside the shop. A 15 gallon tank with one fifth left holds 3 gallons, so the gauge hangs near empty while the car still runs. A recipe built on 2.5 cups of flour needs half a cup when scaled to one fifth, which is 8 tablespoons. A 45 question exam answered at one fifth correct is 9 right answers. A phone showing 20 percent battery is one fifth charged, and the low power warning is doing the same division.

Why fifths end and thirds do not

A fraction in lowest terms produces a terminating decimal only when its denominator has no prime factors other than 2 and 5. The denominator 5 passes that test, so 1/5 stops after one digit. So do 1/20 = 0.05, 1/25 = 0.04, and 1/40 = 0.025, because 20, 25, and 40 are built from 2s and 5s.

Denominators with other prime factors repeat. One third is 0.333..., one seventh is 0.142857142857..., and the block of six digits in the seventh runs forever. The decimal for 1/5 needs no ellipsis and no bar over a digit, which is one reason fifths are easier to quote in prices and in recipes.

The NIST guide to the International System of Units, SP 811 (National Institute of Standards and Technology, 2008) sets the decimal point conventions used in US technical writing, including the leading zero before the point for values below one, as in 0.2 rather than .2. The BIPM SI Brochure (Bureau International des Poids et Mesures, 9th edition, 2019) uses the same decimal marker, so a value copied from a US label into a metric table keeps its meaning.

It helps to see 1/5 next to the denominators on both sides of it. The table below puts each unit fraction into one of two camps, and the boundary between them is the prime factor test from the paragraph above.

The neighbors explain the pattern from both directions. Four and eight are powers of two, so those decimals end, and ten holds a factor of five, so it ends too. Six and nine include a three, and seven is prime with no factor of two or five, so those three repeat. One fifth stays in the terminating camp with room to spare, because its denominator passes the test on the first factor.

Reading 0.2 without slipping a place

The value 0.2 sits one place to the right of the point, so it is two tenths. The value 0.02 sits two places to the right and is two hundredths, twenty times smaller. A trailing zero does not change the value: 0.20 is still 0.2, and 0.200 is still 0.2.

Calculator entry causes most of the errors. One divided by five gives 0.2, while five divided by one gives 5, and the two keystrokes look alike on a phone. If the answer comes out as 5 when you expected a number below one, the numbers went in upside down.

Scale mistakes are the other trap. One fifth of 1,000 is 200, not 20. One fifth of 50 is 10. One fifth of 5 is 1. Reading the decimal as a percent without multiplying by 100 turns 0.2 into 0.2 percent, which is a thousand times too small.

One more check costs nothing. Multiply the decimal back by the denominator. If 0.2 x 5 returns 1, the decimal belongs to 1/5. If it returns 10, the decimal belongs to 10/5 and the entry was wrong.

Estimation gives a second line of defense before any keypad is touched. A fifth of a number is a little more than its sixth and a little less than its quarter, so 0.2 has to sit between 0.1666 and 0.25 on the line. Any answer outside that band points at a slip. The number line drawing on this page shows where the decimal lands and how the fifths march across the tenths in even steps.