1/16 as a Percent

Divide 1 by 16, then shift the decimal

A fraction becomes a percent in two moves. Divide the top number by the bottom number, then multiply the quotient by 100 and attach the percent sign. For 1/16 the division is 1 divided by 16, which comes out to 0.0625, and 0.0625 times 100 is 6.25, so 1/16 is 6.25 percent.

That decimal stops because 16 fits into a power of ten. Multiply 16 by 625 and the product is 10,000, so 1/16 is 625/10,000, which is 0.0625 written in four places. A denominator such as 3 or 7 never divides a power of ten, and those fractions run on without ending. George Mason University's Schar School math refresher (accessed 2026) describes the same two moves: divide for the decimal, then shift the point two places right for the percent.

The percent is a rename of the same share, not a new quantity. One sixteenth of a dollar is 6.25 cents, one sixteenth of an inch is 0.0625 inches, and one sixteenth of any total is 6.25 percent of it. The widget on this page runs the division for the numbers you type and prints the percent, the decimal, the cents out of a dollar and the reduced fraction, so the arithmetic sits in the open instead of being asserted.

Two checks catch most slips. Multiply the percent by the base and divide back: 6.25 percent of 16 is 1, and 1 divided by 16 returns 0.0625. Then watch the decimal point. A result of 0.625 is ten times too large and belongs to 10/16, while 0.00625 is ten times too small and belongs to 1/160.

Sixteenths in a table

Percent, decimal and fraction are three labels for one quantity, and the sixteenths family fills a whole ladder of them. Each rung adds 6.25 percentage points, because every extra sixteenth is one more part out of sixteen equal parts of a hundred.

Four sixteenths is 25 percent, which is a quarter. Eight sixteenths is 50 percent, which is half. Twelve sixteenths is 75 percent, three quarters. Those three rows cover most of the fractions people quote out loud, and the rest of the column fills in the gaps between them.

The reduced forms tell the same story with smaller numbers. 2/16 reduces to 1/8 and reads 12.5 percent, 6/16 reduces to 3/8 and reads 37.5 percent, 10/16 reduces to 5/8 and reads 62.5 percent. Halving a sixteenth gives 1/32 at 3.125 percent, and doubling it gives 1/8 at 12.5 percent. Any row can be checked by dividing the top of the fraction by the bottom and shifting the decimal two places.

The cents column is the percent read as money. A 6.25 percent share of a dollar is 6.25 cents, a 50 percent share is 50 cents, and a 93.75 percent share is 93.75 cents. Nothing in the column depends on the size of the dollar amount, which is why the same numbers work for a $1,200 invoice and for a $16 lunch.

Six point two five percent of a price

Discounts, sales tax and fees all apply a percent to a base, and a sixteenth sits in the range where a lot of everyday rates live. The table takes a few bases and shows the 6.25 percent slice next to what is left.

Take the $80 line. A sixteenth of 80 is 5, so a 6.25 percent discount takes $5.00 off and the register shows $75.00. A 6.25 percent sales tax on the same $80 adds $5.00 instead of removing it, and the total becomes $85.00. Same arithmetic, opposite direction.

The fast route for any base is division by 16. On $240 that is 15, on $1,200 it is 75, and on $4,000 it is 250. The slow route multiplies by 0.0625 and returns the same answers, which is the point: 6.25 percent and one sixteenth are one instruction written two ways.

Working backward is just as quick. If a fee of $15 lands on a $240 order, divide 15 by 240 to get 0.0625, which is 6.25 percent. If the fee were $24 on the same order, the rate would be 10 percent and the fraction would be 1/10 rather than 1/16. The base stayed put while the fee grew, so the rate grew with it.

Sixteenths on a tape measure

A tape measure is where sixteenths earn their keep. The smallest marks on an inch scale cut the inch into sixteen parts, so each mark is 1/16 inch, or 6.25 percent of an inch. NIST Special Publication 811, Appendix B (2008 edition) carries the exact conversion factor: one inch is 25.4 millimeters, so one sixteenth of an inch is 1.5875 millimeters.

Three sixteenths is 0.1875 inch, or 4.7625 millimeters. Fifteen sixteenths, the last mark before the next inch, is 0.9375 inch, or 23.8125 millimeters. A thirty-second, half a mark further, is 0.03125 inch, or 0.79375 millimeters. The millimeter figures come from multiplying the decimal inch by 25.4, the same single step every time.

Fractions of an inch convert to percent like any other fraction, and the percent describes a share of the inch rather than a length in its own right. Half an inch is 50 percent, a quarter is 25 percent, and a sixteenth is 6.25 percent. Reading the scale as percent helps when a plan calls for a gap of a sixteenth and the only ruler in the drawer is marked in millimeters, since 1.5875 millimeters is the number to look for.

Woodworkers lean on the same table when they check a fit. A board that is 1/16 inch proud of its neighbor is off by 6.25 percent of an inch, which sounds small in percent and shows up as a visible ridge on a tabletop. That is the reason a sixteenth is treated as a real error in finish work and as a rounding detail in framing.

The marks around a sixteenth line up in a ladder of their own. Each row below halves or doubles the sixteenth, and the millimeter column comes from one multiplication by 25.4, the factor NIST publishes for the inch.

Reading down the last column, every rung adds 3.125 percentage points, because a thirty-second is half of a sixteenth. The quarter inch row is the anchor most people memorize first, and the other marks hang off it in exact halves.

A sixteenth of an hour, a day and a paycheck

Time divides into sixteenths as neatly as an inch does. An hour holds 60 minutes, and 60 divided by 16 is 3.75, so one sixteenth of an hour is 3 minutes and 45 seconds. Four sixteenths, a quarter hour, is 15 minutes, which agrees with 25 percent of 60.

A day holds 1,440 minutes, and 1,440 divided by 16 is 90, so one sixteenth of a day is 90 minutes, or an hour and a half. A workday of 8 hours is 480 minutes, and a sixteenth of that is 30 minutes, the 6.25 percent of the day that a long meeting eats.

Money follows the same rule at a smaller scale. One sixteenth of a dollar is 6.25 cents, one sixteenth of $16 is $1.00, and one sixteenth of a $1,000 paycheck is $62.50. The units change from minutes to cents to dollars, the division does not.

Bills split sixteen ways use the same share. A $320 dinner divided evenly across sixteen people is $20.00 a head, and a single person's share of that table is 6.25 percent of the total. The percent stays constant while the dollar figure moves with the size of the group and the size of the bill.

The same division runs on clocks and paychecks, where the sixteenth turns a span of time or money into a named slice. Each row is one sixteenth of the total in the middle column.

The hour row explains the 3 minutes 45 seconds figure from the paragraph above, since 0.75 of a minute is 45 seconds. The dinner row is the per head cost when sixteen people split evenly, and it doubles as a check: sixteen shares of $20.00 rebuild the $320.00 total.

Kitchens run on sixteenths without saying so. A cup holds 16 tablespoons, so one sixteenth of a cup is exactly 1 tablespoon, and 3/16 of a cup is 3 tablespoons counted straight from the spoon set. A gallon holds 16 cups, so one sixteenth of a gallon is 1 cup, which turns scaling a 4 cup recipe down by a sixteenth into reading the label on the pitcher.

Reading 6.25 percent as a rate

A 6.25 percent rate on a balance of $1,200 pays $75 for a year under simple interest, because 1,200 times 0.0625 is 75. The same rate on $4,000 pays $250. A 6 percent rate on the $1,200 balance pays $72, so the gap between 6 percent and 6.25 percent is $3 a year on that balance.

Compounding adds a little more. At 6.25 percent a year a balance grows by the factor 1.0625 each year, and 1.0625 squared is 1.12890625, so $1,000 becomes $1,128.91 after two years. The second year earns interest on the first year's interest, which is the whole difference between a simple rate and a compounded one.

The label on a rate matters as much as the digits. A rate quoted per month applies twelve times a year, so 6.25 percent a month costs far more than 6.25 percent a year. Read the time unit in the sentence before comparing two offers, and compare the annual cost of borrowing rather than the headline number.

Percent change uses the same multiplication with a subtraction attached. A price that rises from $80 to $85 has gained $5, and 5 divided by 80 is 0.0625, so the rise is 6.25 percent. A price that falls from $85 to $80 has lost $5, but 5 divided by 85 is 0.0588, so the fall is 5.88 percent. The base moved, and the percent moved with it.

The table spreads that comparison across four balances, all at simple interest for one year. The gap column grows in a straight line with the balance, because both rates are fixed.

Every gap is a quarter of the 6 percent figure, which is the signature of the sixteenth: 6.25 is 6 plus one sixteenth of itself times 4 moved into whole cents. A borrower quoted 6.25 instead of 6 on a $2,400 balance pays $6.00 more over the year, a number worth reading before signing.

Check the answer backward

Every percent on this page can be checked with one multiplication. Take 6.25 percent of 80, which is 5, then divide 5 by 80 and the quotient is 0.0625, the decimal you started from. If the backward step returns 0.625, a decimal point slipped one place to the right and the answer is ten times too large.

A second check reduces the fraction. 6.25/100 is 625/10,000, and dividing both parts by 625 gives 1/16. A percent that came from a fraction should reduce back to that fraction, and when it does not, the percent was rounded somewhere along the way. A rounded 6.3 percent reduces to 63/1,000, which is close to a sixteenth but not equal to it.

A third check looks at size. A sixteenth of a number is smaller than a tenth of it, so 6.25 percent of a base must land below 10 percent of the same base. On $80 the tenth is $8.00 and the sixteenth is $5.00, in the expected order. Numbers that break the ordering, or that fall outside the range between zero and the base, came from a decimal point in the wrong place.