Fraction to Decimal Calculator

Convert a fraction or mixed number to a decimal, or a decimal back to a fraction. Exact digits by long division, the repeating block with its length and starting place, and why the denominator makes it stop or repeat.

Convert Fraction to decimal Decimal to fraction

Fraction or mixed number

A fraction, a mixed number or a whole number: 3/4 · 2 1/3 · 7

Round to

As a decimal

0.833333

Rounded — this decimal repeats forever.

Exact value

0.8(3)

The digits in brackets repeat forever.

In lowest terms

5/6

It was already in lowest terms.

As a percentage

83.33%

0.833333 × 100 — the decimal point moved two places.

The denominator is 6 = 2 × 3, and the 3 in it is what makes this decimal repeat — only 2s and 5s ever stop.

One digit repeats forever: the 3, from decimal place 2 onwards.

How this is worked out

Read the value: 5/6.
Check for a common factor: GCF(5, 6) = 1, so 5/6 is already in lowest terms.
Factor the denominator: 6 = 2 × 3.
The 3 cannot divide a power of ten, so the division never ends.
Divide: 5 ÷ 6 = 0.8(3).
Round to 6 decimal places: 0.833333.

Inch fractions as decimals and millimeters

Fraction	Decimal	Millimeters
	0.015625	0.3969
	0.031250	0.7938
	0.046875	1.1906
	0.062500	1.5875
	0.078125	1.9844
	0.093750	2.3813
	0.109375	2.7781
	0.125000	3.1750
	0.140625	3.5719
	0.156250	3.9688
	0.171875	4.3656
	0.187500	4.7625
	0.203125	5.1594
	0.218750	5.5563
	0.234375	5.9531
	0.250000	6.3500
	0.265625	6.7469
	0.281250	7.1438
	0.296875	7.5406
	0.312500	7.9375
	0.328125	8.3344
	0.343750	8.7313
	0.359375	9.1281
	0.375000	9.5250
	0.390625	9.9219
	0.406250	10.3188
	0.421875	10.7156
	0.437500	11.1125
	0.453125	11.5094
	0.468750	11.9063
	0.484375	12.3031
	0.500000	12.7000
	0.515625	13.0969
	0.531250	13.4938
	0.546875	13.8906
	0.562500	14.2875
	0.578125	14.6844
	0.593750	15.0813
	0.609375	15.4781
	0.625000	15.8750
	0.640625	16.2719
	0.656250	16.6688
	0.671875	17.0656
	0.687500	17.4625
	0.703125	17.8594
	0.718750	18.2563
	0.734375	18.6531
	0.750000	19.0500
	0.765625	19.4469
	0.781250	19.8438
	0.796875	20.2406
	0.812500	20.6375
	0.828125	21.0344
	0.843750	21.4313
	0.859375	21.8281
	0.875000	22.2250
	0.890625	22.6219
	0.906250	23.0188
	0.921875	23.4156
	0.937500	23.8125
	0.953125	24.2094
	0.968750	24.6063
	0.984375	25.0031
	1.000000	25.4000

1 inch = 25.4 mm exactly. Press a fraction to load it into the box above.

Nearest fraction on a tape measure

Ruler step	Nearest fraction	Difference
1/2	1/2	0.125000
1/4	1/2	0.125000
1/8	3/8	0.000000
1/16	3/8	0.000000
1/32	3/8	0.000000
1/64	3/8	0.000000

Once a finer step stops changing the answer, the extra marks on the tape are not helping you.

Updated: September 12, 2026

Fraction to decimal converter. The exact decimal, and whether it stops or repeats.

A fraction-to-decimal calculator divides the top number by the bottom one and reports whether that decimal stops or repeats forever. It runs both ways: type 5/6 and the cards read 0.833333, 0.8(3) and 83.33%, or switch to Decimal to fraction and 0.375 comes back as 3/8.

What a Fraction to Decimal Conversion Actually Answers

Converting a fraction to a decimal means dividing the top number by the bottom one, and the division ends in one of two ways. It stops after a fixed number of places, the way 3/8 stops at 0.375, or it settles into a block of digits that runs forever, the way 5/6 settles into 0.833333… — written here as 0.8(3), with the repeating digits in brackets.

Which of the two happens is settled by the denominator before any dividing starts. Reduce the fraction to lowest terms and factor what is underneath: a denominator built only from 2s and 5s, the two primes that multiply to ten, always stops, and any other prime in there makes the decimal run forever. The page shows that working instead of announcing a verdict. For 5/6 the line under the cards names the factorization, 6 = 2 × 3, and points at the 3 as the reason. Wikipedia's article on repeating decimals states the same condition, and Common Core standard 8.NS.A.1 asks eighth-graders to show that a rational number's decimal expansion repeats eventually and to convert such an expansion back into a fraction — which is both directions of this page.

The reverse direction carries a trap. 0.375 is exactly 3/8 and nothing is lost on the way. 0.333 is exactly 333/1000, yet almost nobody who types 0.333 means 333/1000; they mean a third that something already rounded. Both answers sit on screen at once: the hero card gives the exact fraction, and a card called Simplest close fraction offers the closest fraction with a denominator under 100 along with the real gap between the two. For 0.333 that is 1/3, sitting 0.000333 above what was typed. The cap of 100 is what makes the second card worth having — allow denominators up to 1000 and the closest fraction to 0.333 is 333/1000 again, which helps nobody.

Every digit comes out of whole-number arithmetic. Ask for 1/7 at 20 decimal places and the answer is 0.14285714285714285714; the same division through a floating-point number drifts from the 17th digit on. That gap reaches the inch chart at the bottom of the page as well: 16 of its 64 rows land on an exact tie at the fourth millimeter decimal, and a floating-point route rounds 13 of them the wrong way — 19/32 of an inch is 15.0813 mm where a float prints 15.0812.

One value goes in and one comes out. Arithmetic on two fractions — quarters plus thirds, a common denominator, dividing by a sixth — is the fraction calculator's job, and that page prints its answer as a decimal too. The split is deliberate: there the decimal is a by-product of the sum, and here the decimal is the question, which is why the repeating block, its length and its starting place live on this page.

How to Use the Fraction to Decimal Converter

Nothing needs submitting: 5/6 is already in the box with its answer under it, and every keystroke redraws the cards.

1. Pick a direction. The first control is labeled Convert and carries two pills, Fraction to decimal and Decimal to fraction. Each direction keeps its own box, so switching between them can never drop you onto an error message — whatever you left in the other box is still waiting there.

2. Type the value. The box labeled Fraction or mixed number takes a fraction (3/4), a mixed number written with a space between the parts (2 1/3) or a whole number (7). One minus in front owns the whole value, so -2 3/4 is minus two and three quarters, which the steps expand to -11/4. The box labeled Decimal takes 0.375, -2.75, and a repeating decimal with its block in brackets at the very end: 0.1(6).

3. Choose the precision. The Round to select opens at 6 decimal places and runs from a whole number up to 30. Rounding is half-up and it happens on whole numbers, so the digit in the last place you asked for is the digit that belongs there.

4. Read the cards. Converting a fraction they are As a decimal, Exact value, In lowest terms and As a percentage. Converting a decimal they are As a fraction, As a mixed number, Simplest close fraction and As a percentage. Each carries one line underneath saying where its number came from. Simplest close fraction steps aside when the closest fraction under 100 is already the exact answer, which is why 0.375 shows three cards and 0.333 shows four.

5. Read the verdict under the cards. One sentence names the denominator's factorization and the prime that decides the outcome. For a repeating decimal a caption underneath names the block, counts its digits and says which decimal place it starts at — for 5/6, one digit repeats, the 3, from decimal place 2 onwards.

6. Work down the steps. The list titled How this is worked out is open when the page loads. Going fraction to decimal it reads the value, reduces it, factors the denominator, gives the verdict, divides and rounds. Going the other way it reads the decimal, writes it over a power of ten (or clears the repeat by subtraction), divides by the GCF, converts to a mixed number and works out the percentage.

7. Use the table as a shortcut. Under the steps sits a 64-row chart of inch fractions with their decimals and millimeters, and every fraction in it is a button — pressing 19/32 loads 19/32 into the box above. In the decimal direction the table becomes the six ruler steps from halves to sixty-fourths, with the nearest fraction at each one and how far off it lands.

The Rule That Decides Whether a Decimal Stops

\frac{n}{d} \text{ terminates} \iff d = 2^{a} \cdot 5^{b}

$n$ = Numerator of the fraction after it has been reduced to lowest terms
$d$ = Denominator after reducing — the only number that decides whether the decimal stops
$a$ = How many times 2 divides that denominator, or zero if it does not
$b$ = How many times 5 divides that denominator, or zero if it does not

Reducing first is not optional, because the test reads the denominator the fraction has after reducing and not the one that was typed. A denominator of 12 carries a 3 and looks like a repeater, yet 6/12 is a half once the common factor comes out, and a half stops at 0.5. The page reduces before it factors, and the In lowest terms card names the factor it divided by so you can follow the move.

When a decimal does stop, the number of places it takes is max(a, b), the larger of the two exponents. 3/8 has 2³ underneath and no 5s, so it stops at three places, 0.375; 1/64 has 2⁶ and stops at six, 0.015625. When it repeats, those same two exponents count the digits that stand in front of the block: 5/6 carries one factor of 2 and no 5, so exactly one digit comes first, the 8 in 0.8(3).

The length of the block is a separate quantity. Strip every 2 and every 5 out of the denominator and the period is the multiplicative order of 10 modulo what is left — the smallest power of ten that leaves a remainder of 1. Wolfram MathWorld lists the periods of 1/n outright: 6 for 1/7, 16 for 1/17, 18 for 1/19. Wikipedia supplies the ceiling, that the period of 1/k is never longer than k − 1, which 1/7 reaches exactly.

Going from a repeating decimal back to a fraction runs on one identity. Multiply by the power of ten that shifts exactly one block past the point, subtract the unshifted number so the infinite tails cancel, and divide:

0.\overline{3} = \frac{3}{9} = \frac{1}{3}

With lead-in digits in front of the block, the same subtraction leaves nines for the block and zeros for the lead-in. 0.1(6) becomes (16 − 1) ÷ 90 = 15/90 = 1/6, which is the line the page prints under the fraction card. Written generally, it is the number with one block minus the number without it, over as many nines as the block is long followed by as many zeros as there are lead-in digits.

US classrooms usually draw a bar over the repeating digits instead of bracketing them:

0.8\overline{3}

That is the same value this page writes 0.8(3).

How to Convert a Fraction to a Decimal by Hand

Three methods cover almost everything, and which one is quickest depends on the denominator.

1. Divide. The fraction bar means divided by, so 3/8 is 3 ÷ 8. Long division reaches 0.375 in three steps and halts there, because the remainder hits zero.

2. Make the denominator a power of ten. This beats long division whenever the denominator divides 10, 100 or 1000. Multiply the top and bottom of 3/8 by 125 and it becomes 375/1000, which is read off as 0.375 with no dividing at all. The method works only when the decimal terminates, which is the same condition as before.

3. Learn the small ones. Eighths, sixteenths, sixths and thirds come up so often that spotting them beats any method: 1/8 = 0.125, 3/16 = 0.1875, 5/8 = 0.625, 1/3 = 0.333…

Going the other way splits in two. A decimal that stops is already a fraction over a power of ten: 0.375 is 375 thousandths, so write 375/1000 and divide both parts by GCF(375, 1000) = 125 to reach 3/8. That is exactly the arithmetic the page prints in the reverse direction, GCF and all, and the same three moves turn 0.125 into 125/1000 and then 1/8.

A repeating decimal needs the subtraction trick instead. Call the number x and multiply by the two powers of ten that line the repeating tails up, then subtract so they cancel. For 0.1(6): 100x is 16.666… and 10x is 1.666…, so 90x = 15 and x = 15/90, which reduces to 1/6. The page prints the same identity in one line as (16 − 1) ÷ 90. This is the move Common Core 8.NS.A.1 asks for by name, and Illustrative Mathematics sets it as a classroom task under that standard.

Common Fractions, Their Decimals and the Verdict

Fraction	At 6 decimal places	Exact value	Stops or repeats
1/2	0.500000	0.5	Stops — denominator 2
3/8	0.375000	0.375	Stops — 8 = 2 × 2 × 2
5/8	0.625000	0.625	Stops — 8 = 2 × 2 × 2
3/16	0.187500	0.1875	Stops — 16 = 2 × 2 × 2 × 2
11/16	0.687500	0.6875	Stops — 16 = 2 × 2 × 2 × 2
1/64	0.015625	0.015625	Stops — 64 = 2 × 2 × 2 × 2 × 2 × 2
1/3	0.333333	0.(3)	Repeats — denominator 3
5/6	0.833333	0.8(3)	Repeats — 6 = 2 × 3
1/7	0.142857	0.(142857)	Repeats — denominator 7
21/98	0.214286	0.2(142857)	Repeats — reduces to 3/14, and 14 = 2 × 7

Worked Conversions, Both Directions

5/6, the conversion the page opens with

Load the page and 5/6 is already in the box with its answer underneath. At the default six decimal places the hero card reads 0.833333, and its line says the value was rounded because the decimal repeats forever. The Exact value card carries the whole truth in six characters: 0.8(3). In lowest terms reports 5/6 unchanged, since 5 and 6 share no factor, and the percentage card reads 83.33%.

The sentence under the cards is where the page earns its keep. It names the denominator as 6 = 2 × 3 and points at the 3, because a denominator built only from 2s and 5s stops and this one is not. The caption below counts the repeat — one digit, the 3, from decimal place 2 onwards — and that starting place is not arbitrary: the single factor of 2 in the denominator is what puts exactly one digit in front of the block.

1/7 and its six-digit block

1/7 is the fraction that makes a repeating block visible. The decimal card shows 0.142857 at six places, which looks like a clean stop until you read the Exact value card: 0.(142857), brackets around all six digits with nothing in front of them. The block starts at the first decimal place because 7 carries no factor of 2 or 5 at all.

Six digits is the longest a seventh could possibly have. Wikipedia puts the ceiling for 1/k at k − 1, and Wolfram MathWorld lists the period of 1/7 as 6, so this one runs the full distance. Ask for 20 decimal places and the answer is 0.14285714285714285714, the six-digit block three times over and two digits more, with no drift. A floating-point calculator handed the same division goes wrong from the 17th digit onwards.

21/98, where reducing changes the answer

98 factors as 2 × 7 × 7, which looks like a lot of sevens, but the rule applies to the reduced fraction and not to what you typed. GCF(21, 98) = 7, so 21/98 is 3/14 and the denominator under test is 14 = 2 × 7. One 7 is enough to settle it.

The cards read 0.214286 at six places, 3/14 in lowest terms and 21.43%, and the exact form is 0.2(142857) — the same six digits as a seventh, with a 2 standing in front of them. The single factor of 2 in 14 pushes the block one place to the right, so the repeat starts at the second decimal place rather than the first. The same six digits turning up in both 1/7 and 3/14 is not a coincidence: strip the 2 out of 14 and a 7 is what is left.

0.333 back to a fraction, exactly and approximately

Switch to Decimal to fraction and type 0.333. The hero card answers 333/1000, which is what the digits literally say, and the worked steps show the arithmetic: the number written over a thousand, then a GCF of 1, so nothing reduces. The percentage card reads 33.3%.

Simplest close fraction is the card that matters here. It offers 1/3, the closest fraction anywhere with a denominator under 100, and states the gap out loud: 0.000333. Which of the two you want depends on where the number came from — 0.333 read off a ruler or a gauge really is 333/1000, while a 0.333 that came out of somebody else's calculator was a third before it was rounded. Type 0.8333 instead and the same pair appears: 8333/10000 exactly, with 5/6 beside it, 0.000033 apart.

3.14159 and the closest fraction under 100

A decimal with a whole part fills the mixed-number card too. 3.14159 gives 314159/100000 as the exact fraction, 3 14159/100000 as the mixed number and 314.16% as the percentage. The exact fraction does not reduce, because 314159 and 100000 share no factor.

Simplest close fraction answers 311/99 and reports the difference as -0.000176, the minus sign meaning the fraction sits just below what was typed. That figure is what makes the card usable when 3.14159 is a dimension rather than a constant: a fraction with two digits underneath, landing within two ten-thousandths, is often close enough to work with, and the card says precisely how much is being given up.

-2 3/4 and the round trip

Type -2 3/4 into the fraction box and the sign is read as owning the whole value. The steps expand it as -(2 × 4 + 3)/4 = -11/4 rather than as minus two plus three quarters. The decimal card reads -2.750000 at six places, the Exact value card -2.75, In lowest terms -11/4 and the percentage -275%. The denominator 4 = 2 × 2 carries nothing but 2s, so the decimal stops after two places.

Now switch to Decimal to fraction and type -2.75. The trip reverses cleanly: -11/4 as the fraction, -2 3/4 as the mixed number, -275% again. Simplest close fraction stays out of sight this time, because -11/4 is already the simplest fraction with a denominator under 100 and there is nothing closer to offer.

0.4 inches on a tape measure

Type 0.4 into the decimal box and the table under the cards walks down the ruler. At halves and again at quarters the nearest mark is 1/2, a full 0.1 above the number you typed. At eighths and at sixteenths it is 3/8, 0.025 below. At thirty-seconds and sixty-fourths it settles on 13/32, 0.00625 above.

The repeated rows are the useful part of that table. Two steps giving the same fraction means the finer marks stopped changing the answer, so 3/8 is the best a sixteenth tape can do and 13/32 is as close as a thirty-second gets. A tape is marked in halves down through sixty-fourths and 0.4 lands on none of them, which is the whole reason the table is there.

Where This Page Stops

Two boxes, one value in each. There is no expression to type into, no brackets for grouping and no operator precedence, so a calculation with several steps in it belongs on the fraction calculator, which works in pairs and can feed its own answer back in.

Every number stays under eight digits, with a ceiling of 9,999,999 per part inherited from the fraction parser. That bites the decimal box in a way worth knowing about: type seven digits after the point and the fraction behind them usually needs a denominator of 10,000,000, one digit past the ceiling, so a value like 0.1234567 comes back as dashes in every card unless it happens to reduce. Six digits after the point is the comfortable working width — 0.142857 converts without complaint and lands on 1/7 as its closest simple fraction.

The page looks 200 digits deep for a repeating block and never reports a length it did not find. 1/97 has a block of 96 digits, which is inside the window, so the length is found and stated even though the Exact value card has room for only the first two dozen digits and closes with an ellipsis. 1/9999991 repeats with a block far longer than the window: the verdict still says it repeats, because that comes from the factors rather than from the search, but the Exact value card shows a dash and the caption says the block is longer than 200 digits instead of guessing a number.

The notation is brackets rather than a bar. Wikipedia's article on repeating decimals records three conventions in use — a bar over the repeating digits in the United States, Canada, India, France and Germany among others, dots above the outer digits in the United Kingdom, Japan, China and elsewhere, and brackets around the repeating part, which is the form the article's own example 0.58(3) uses. Brackets are what the Decimal box can read back, so a value copied from a card pastes straight into the other direction. Homework usually wants whichever form the class was taught.

Simplest close fraction stops at a denominator of 99, and that limit is the point of the card rather than a shortfall in it. The percentage is the one figure rounded for display, to two decimals, with extra decimals shown when two would print as 0%.

Shortcuts Worth Knowing

Reduce before you judge the denominator. 21/98 looks like it is about sevenths and it is, but only after GCF(21, 98) = 7 turns it into 3/14. The In lowest terms card names the factor it divided by, so the reduction is something you can check rather than assume.
Press a chart row instead of typing. Every fraction in the inch table is a button, so 19/32 loads with one press and cannot arrive as 19/23.
Copy the exact value and paste it into the other direction. 0.8(3) taken from the Exact value card goes straight into the Decimal box and comes back as 5/6. The brackets exist so that round trip works.
Read the difference before you round a measurement. Simplest close fraction says how far its answer sits from what you typed: 0.000333 for 0.333, 0.000033 for 0.8333. If that gap is inside your tolerance, take the friendly fraction; if it is not, keep the exact one.
Carry the fraction and round on the last line. A repeating decimal cut at six places has already lost something. When the value feeds a longer calculation, keep 5/6 and convert at the end rather than at the start.
Ask for more places when a decimal looks suspiciously short. A decimal can stop and still be long, and the card tells you how many places the exact value runs to whenever six are not enough to show it.
Send the link rather than a screenshot. The direction, the value and the precision all travel in the address bar, so a link copied from Decimal to fraction reopens on that pill with the same number in the box. Only the untouched default state has no query string.

The Words This Page Uses

Repetend

The block of digits that repeats forever. In 0.(142857) the repetend is 142857; in 0.8(3) it is the single digit 3. The brackets on screen mark exactly this.

Period

How many digits long the repetend is. 1/7 has a period of 6, 1/17 a period of 16 and 1/19 a period of 18, and no fraction with denominator d can have a period longer than d − 1.

Lead-in digits

The digits between the decimal point and the start of the repeating block. 5/6 is 0.8(3), so it has one, which is why its block begins at decimal place 2. 1/7 has none and its block begins at place 1.

Terminating decimal

A decimal that stops. A reduced fraction gives one exactly when its denominator is built from 2s and 5s alone, so 1/64 terminates at 0.015625 while 1/3 never does.

Vinculum

The bar drawn over the repeating digits in US and many European classrooms. It means the same thing as the brackets this page prints.

Decimal fraction

A fraction whose denominator is a power of ten. Every decimal that stops is one before it is reduced: 0.375 read literally is 375/1000, which then divides down to 3/8.

Simplest close fraction

The page's name for the closest fraction with a denominator under 100, shown with the distance between it and the value you typed. For 0.333 it is 1/3; for 3.14159 it is 311/99.

Questions About Fractions and Decimals

How can I tell whether a fraction gives a terminating decimal without dividing?

Reduce it, then factor the denominator. If the only primes left are 2 and 5, the decimal stops; any other prime makes it repeat. 3/8 stops because 8 = 2 × 2 × 2. 5/6 repeats because 6 = 2 × 3.

What is 5/6 as a decimal?

0.833333 at six decimal places, and 0.8(3) exactly: one digit repeats forever, the 3, from the second decimal place onwards. As a percentage it is 83.33%.

What is 2 1/3 as a decimal?

2.333333 at six places, written exactly as 2.(3). The mixed number becomes 7/3 first, and because 3 is neither a 2 nor a 5 the division never ends. The percentage card reads 233.33%.

How many digits repeat in 1/7?

Six. The block is 142857 and it starts at the first decimal place, so 1/7 is 0.(142857). Wolfram MathWorld lists the same period, alongside 16 for 1/17 and 18 for 1/19.

Is 0.333 the same as 1/3?

Not quite. Typed as written, 0.333 is exactly 333/1000, and that is the fraction the hero card gives. Simplest close fraction offers 1/3 beside it with the gap spelled out, 0.000333. A 0.333 that came off a gauge or a ruler really is 333/1000; a 0.333 that came out of another calculator was a third before somebody rounded it, and then 1/3 is the number you want.

How do I type a repeating decimal into the Decimal box?

Put the repeating digits in brackets at the very end: 0.1(6) for a sixth, 0.(3) for a third, 0.(142857) for a seventh. It is one field, with no separate box for the repeating part. A block of zeros is not a repeat, so 0.5(0) is turned down with a note asking you to drop the brackets, and an unclosed bracket such as 0.1(6 is turned down too.

Why does the page write 0.8(3) instead of putting a bar over the 3?

Both notations mean the same value. Wikipedia's article on repeating decimals records a bar over the repeating digits as the convention in the United States, Canada, India, France and Germany among others, dots above the outer digits in the United Kingdom, Japan, China and elsewhere, and brackets around the repeating part, which is the form its own example 0.58(3) uses. Brackets are what this page's Decimal box can read back, so a value copied from a card can be pasted into the other direction and converted again. If your class wants the bar, write the 0.8 and draw the bar over the 3.

Why does my phone calculator show 0.142857142857142849 for 1/7?

It is holding the value as a binary floating-point number, and a seventh has no exact binary form. Ask for 20 decimal places here and every one of them is right — 0.14285714285714285714 — because the division runs on whole numbers with no floating-point step in the chain. The same gap shows up in the millimeter column of the inch chart, where a floating-point route rounds 13 of the 64 rows the wrong way: 19/32 of an inch is 15.0813 mm, which a float prints as 15.0812.

What is 19/32 of an inch in millimeters?

15.0813 mm. The inch has been exactly 25.4 mm since the 1959 international agreement, which NIST records as a definition rather than a measurement, so the whole column is exact arithmetic. The chart under the calculator carries all 64 sixty-fourths with their decimals and millimeters.

Which tape-measure mark is closest to 0.4 inches?

3/8, at both eighths and sixteenths, sitting 0.025 under 0.4. Go finer and it becomes 13/32, 0.00625 over, at both thirty-seconds and sixty-fourths. Halves and quarters both round up to 1/2, a full 0.1 too big. The table repeats a row on purpose: once a finer step stops changing the answer, the extra marks on the tape are not doing anything for you.

How many decimal places can I ask for?

Twelve options on the Round to select: a whole number, then 1 through 6, then 8, 10, 15, 20 and 30 decimal places, opening at 6. Rounding is half-up and it is done on whole numbers, so the last digit you asked for is genuinely the last digit. A decimal can also stop well past 6 — 1/8388608 runs to exactly 23 places — and in that case the card says how long the exact value is rather than letting six places pass for the whole answer.

Does 0.999... equal 1?

Yes, and this page gets there with no special case. Type 0.(9) into the Decimal box and the subtraction it performs is (9 − 0) ÷ 9, which is nine ninths, one whole. Illustrative Mathematics sets the same question as a task under Common Core 8.NS.A.1 with the same algebra: if x = 0.999..., then 10x = 9 + x, so 9x = 9 and x = 9/9.

Sources & References

Content verified by the Smart Calculators Team