15/16 as a Decimal

Divide 15 by 16 and the decimal stops at four places

To turn 15/16 into a decimal, divide 15 by 16. Sixteen does not fit into 15, so the answer starts with 0. and the work moves to the tenths: 150 divided by 16 is 9 with 6 left over. Bring down the next zero and 60 divided by 16 is 3 with 12 left over. Then 120 divided by 16 is 7 with 8 left over, and finally 80 divided by 16 is 5 with nothing left over. A zero remainder closes the division.

Because the remainder lands on 0, the decimal stops: 15/16 = 0.9375. Four digits, no dots, no repeating block. The check runs backward without a calculator: 0.9375 x 16 = 15, so multiplying the decimal by the denominator returns the numerator.

The reason it ends is sitting in the denominator. Write 16 as primes and you get 2 x 2 x 2 x 2, nothing but twos. A fraction in lowest terms terminates as a decimal when its denominator carries no prime other than 2 or 5, because those are the only prime factors a power of ten has. Fifteen over sixteen is already in lowest terms, since the greatest common divisor of 15 and 16 is 1, so the rule applies without any reducing step. Set the same numerator over 9 and the story changes: 15/9 reduces to 5/3, and 5/3 repeats forever as 1.666..., because the 3 in the denominator can never divide a power of ten.

The sixteenths family from 1/16 to 16/16

Every sixteenth has a clean four place decimal, which makes the whole family easy to carry in your head. Each sixteenth is worth 0.0625, and each step in percent is 6.25%. Fifteen sixteenths is the second to last row.

The last row before the top doubles as a shortcut: 15/16 is 1 minus 1/16, and 1 minus 0.0625 is 0.9375. Any sixteenth you forget can be rebuilt that way, or by halving: half of 0.0625 is 0.03125 for a thirty second, and half again is 0.015625 for a sixty fourth.

Pairs give a quick self check. 1/16 plus 15/16 is 1, and 0.0625 plus 0.9375 is exactly 1 with nothing lost. The same pairing holds down the table: 7/16 with 9/16, and 3/16 with 13/16. If two sixteenths sum to a whole number, their decimals must sum to a whole number too, and any row that fails that test was copied wrong.

As a percent: 93.75%

Multiply the decimal by 100 and 15/16 reads as 93.75%. No rounding is involved, because the exact decimal has four places and the percent form needs only two.

On money the fraction pays in round numbers whenever the base divides by 16. Take a $1,280 invoice and pay 15/16 of it: 1,280 divided by 16 is $80 per sixteenth, and 15 sixteenths is $1,200.00. The $80 still owed is the exact 6.25% the fraction leaves behind. The panel on this page prices any fraction of any amount the same way.

Word choice matters as much as the arithmetic. A quote of "about 94%" is not the same promise as fifteen sixteenths: 94% of $1,280 is $1,203.20, which is $3.20 above the exact share. On a $1,280 bill the drift is pocket change, but the gap grows in step with the base, so a contract that means 15/16 should say 15/16 or 93.75% and not a rounded neighbor.

Rounding 0.9375 and what each place is worth

The exact decimal 0.9375 needs four places, so any shorter write up is a rounded one. Two places give 0.94, three give 0.938, four give the value back with nothing lost. The table prices each option on a base of $90,000, where the rounding gap is large enough to see.

The worked example behind the table: 90,000 divided by 16 is 5,625 per sixteenth, and 15 x 5,625 = 84,375, the exact answer. Two place rounding drifts $225 high because 0.94 sits 0.0025 above 0.9375, and 0.0025 x 90,000 = 225. Each extra decimal place cuts the error by a factor of ten, which is the standard behavior the NIST rounding conventions in Special Publication 811 describe for published figures: carry more places than you print, and round once at the end.

One more habit worth copying from that rule: keep the exact fraction through the middle of a chain of calculations and convert to a rounded decimal only at the last step. Multiplying rounded decimals compounds the drift, while one final rounding cannot.

On the ruler and in the shop: inches and millimeters

On a ruler marked in sixteenths, 15/16 is the last mark before the 1. In millimeters the value is 0.9375 x 25.4 = 23.8125 mm, exact rather than approximate, because the inch has been fixed at 25.4 mm by the international agreement on measurement units since 1959.

The shop version of the same number is a socket. A 15/16 inch wrench sits 0.1875 mm below a 24 mm metric wrench, close enough that the two get swapped in a pinch, though the fit goes loose on a worn fastener. The size earns its spot in a US socket set for plainer reasons: the hex nut on a 5/8 inch fastener measures 15/16 inch across the flats, so anyone tightening a 5/8 inch bolt reaches for it.

Reading the fraction off the ruler is where mixups start. The midpoint of the inch is 8/16, the mark labeled 1/2, and 15/16 sits seven marks later, one short of the end. Count marks rather than eyeballing: on a crowded sixteenth scale, the second to last mark is easy to misread as 7/8, which is 0.875 and a whole sixteenth smaller.

Kitchen, time and distance conversions

Fifteen sixteenths lands on friendly numbers in several everyday units, because so many of them hold 16 parts.

The cup row is the one cooks use. A recipe asking for 15/16 cup is asking for 15 tablespoons, and since 16 tablespoons fill the cup, the missing tablespoon is the 1/16. Measure 15 level tablespoons and skip the awkward nearly full cup line.

The hour row works the same way in minutes. 3,600 seconds divided by 16 is 225 seconds per sixteenth, and 15 of them is 3,375 seconds, which is 56.25 minutes or 56 minutes 15 seconds. The mile row rounds less neatly but stays whole: 5,280 feet divided by 16 is 330 feet per sixteenth, and 15 x 330 = 4,950, exactly 150 feet under the full mile.

Where 15/16 gets misread

Four misreads cover most of the wrong answers written for this fraction.

Dropping a digit. 0.09375 is 15/160, not 15/16, one tenth of the right value. The give away is size: fifteen sixteenths is nearly a whole, so the decimal must start with 0.9, never 0.0.

Swapping in a nearby percent. On a $90,000 base, 95% is $85,500 while 15/16 is $84,375, a gap of $1,125. The two numbers sit close enough to pass on sight and far enough apart to matter on a contract.

Truncating instead of rounding. 0.93 x 16 = 14.88, so a decimal that fails the multiply back test is not a sixteenth at all. Any honest sixteenth times 16 returns a whole number, and 0.9375 passes with 15.

Flipping the fraction. 16/15 = 1.0666..., a number greater than 1, while 15/16 is less than 1. If your decimal crosses 1, the numerator and denominator traded places somewhere.

One ruler note closes the list: 15/16 is not the middle of the inch, it is the last sixteenth mark before the end. The middle mark reads 8/16 and gets labeled 1/2. On a tape measure crowded with marks, counting from 1 rather than trusting a glance settles it.