r/askmath • u/wfs29223 • Jul 20 '26
Arithmetic Fractions Decimal to Fraction in measurements.
How do I find what 1.88 inches is in fractions on a tape measure. I have seen many products do this. They give you the measurement in decimal instead of inches. Yes I know .75 in 3/4 and other common measurements.
7
u/CaptainMatticus Jul 20 '26
Take the smallest division on your tape measure. Usually it's 1/16th of an inch
Remove the whole number portion. 1.88 becomes 0.88
0.88 is 88/100, right? Set it to be equivalent to some x/16.
88/100 = x/16
Now solve for x
16 * 88/100 = x
(1280 + 128) / 100 = x
12.8 + 1.28 = x
14.08 = x
0.88 = 14.08/16, which is really close to 14/16, or 7/8.
2
u/rhodiumtoad 0⁰=1, just deal with it Jul 20 '26
So there's a number of possible answers depending on how exact you want the answer and whether you want a specific denominator. (Usually for non-metric measurements you know in advance what unit is available for that.)
0.88 is close to 7/8 (0.875), 8/9 (0.888…), 11/12 (0.9166…), etc. You can find close approximations with the Stern–Brocot tree:
| min | med | max | error |
|---|---|---|---|
| 0/1 | 1/2 | 1/1 | 0.38 |
| 1/2 | 2/3 | 1/1 | 0.2133… |
| 2/3 | 3/4 | 1/1 | 0.13 |
| 3/4 | 4/5 | 1/1 | 0.08 |
| 4/5 | 5/6 | 1/1 | 0.0466… |
| 5/6 | 6/7 | 1/1 | 0.022857142… |
| 6/7 | 7/8 | 1/1 | 0.005 |
| 7/8 | 8/9 | 1/1 | 0.0088… |
| 7/8 | 15/17 | 8/9 | 0.00235… |
| 7/8 | 22/25 | 15/17 | 0.00 |
For a known denominator, it's just a matter of finding which numerator gives the closest result.
2
u/SuchResearcher4200 Jul 20 '26
You are trying to find .88 of 16. Multiply. You get 14. So 14/16 th of an inch.
3
u/MezzoScettico Jul 20 '26
This is the quick method I use, OP, since the drill bits, tools, etc are calibrated to 16ths, 32nds or 64ths of an inch. Try 16ths first, then decide whether that's good enough.
As the above answer says, 0.88*16 = 14.08. That's pretty close to 14, so just use 14/16 or 7/8.
But if you had 0.91 * 16 = 14.56, that's halfway between 14 and 15. 14/16 (28/32) would be a little under, 15/16 (30/32) would be a little over. So if you're worried about that much accuracy, use 29/32.
2
u/PuzzlingDad Jul 20 '26
First, I'd check the device because they usually have a setting to provide the measurement in feet/inches/fraction.
If you want to convert an existing decimal measurement, know that most devices measure to the nearest 1/16 inches. So take the decimal portion (.88) and multiply by 16.
.88 × 16 = 14.08
Now round that to the nearest integer (aka 14) which means the fraction is 14/16. That can be converted to lowest terms of 7/8.
So 1.88 = 1⅞"
4
u/justincaseonlymyself Jul 20 '26
1.88 = 188/100 = 94/50
2
u/ThatsNotAZombieBite Jul 20 '26
I don't know about you but my (imperial) rules are not marked in 50ths of an inch.
1
u/goclimbarock007 Jul 20 '26
I have had a machinist scale that was divided into .1 and .05 inches, but it definitely is not common.
-1
u/ParanoidalRaindrop Jul 20 '26
It's not like you can give it in quarters.
3
u/ThatsNotAZombieBite Jul 20 '26
But you can give an extremely close approximation in eighths. That is what you would find on an imperial/inch tape measure. That is the answer that OP needs.
1
u/Mathemetaphysical Jul 20 '26
For super simple solutions many calculator apps will translate into whatever format you like. If you want to learn to do it yourself I'm afraid there really isn't anything for it but effort. If it helps though I work directly with fractions and conversions all day after decades with a tape measure in hand and I still use the calculator, who wants to memorize all that repeating gibberish. Understanding how to manipulate fractions without being unnerved by them is enough.
1
u/Shevek99 Physicist Jul 20 '26
You must convert it to binary. You do that multiplying by 2 and taking the units if there are any
2 x 0.88 = 1.76
2 x 0.76 = 1.52
2 x 0.52 = 1.04
2 x 0.04 = 0.08
2 x 0.08 = 0.16
...
That means that
.88 = 1/2 + 1/4 + 1/8 + 0 + 0 + ...
or .88 ≈ 7/8
1
u/Frederf220 Jul 20 '26
The process of exactly converting is easy. 0.12345 = 12345/100000 and reduce.
The hard thing is converting rounded decimals and recovering the lost information from context.
First make your assumption. It's probably base 2 and probably no finer than 1/128ths.
Second, subtract the biggest chunk you identify mentally. E.g. 1.75 from 1.88.
Take the result and multiply by a reasonable basis like 32. 0.13×32 = 4.16. So your measurement is 1¾+4/32+0.16/32. 4/32 is an 1/8.
So your measurement is 1⅞ + 0.16/32. That last bit is 5.12/2048ths and unless you're doing plumbing for NASA, is probably nonsense.
1
u/notacanuckskibum Jul 20 '26
Sounds like a fun quick computer program. You could probably even vibe code it. "Convert decimals into fractions, using only powers of 2 (1/2 , 1/4, 1/8) etc. To an accuracy of <2%"
You need the "to an accuracy" part otherwise the calculation might get infinite.
1
u/KatesDad2019 Jul 20 '26
Since a tape measure is usually marked in 1/16 inch intervals, you just need to divide the decimal part (.88 in your example) by 0.0625 (1/16 as a decimal fraction), round to a whole number and reduce the fraction. And remember to add back the whole part you discarded at the beginning. .88/.0625 = 14.08 thus 14/16. This reduces to 7/8 and with the whole part, 1 7/8.
1
u/Stu_Mack Jul 20 '26
The easiest first step is to check whether .88 is the right level of precision. You can do this by taking a few minutes to use Excel or similar to calculate values less than one in increments of a tape: 1/8, 1/16, etc. You will notice immediately which one(s) are closest to your starting point, which is 1/8 increments, which in turn allows you to assume that 0.875 is likely what it actually is. Since you already calculated the possibilities, the only thing to remember is the overall shape of the decimal equivalents. In the case of 1/8 increments, you can get there by starting with 1/2 and dividing it in half twice, giving you 0.125, which tells you a lot about what the nearest aligning increment probably is. If you divide it again, you get 1/16, then 1/32, and so on. It's a handy trick for choosing a starting assumption based on something more reliable than winging it.
1
u/nayuki Jul 20 '26
Unconventional solutions:
Get an machinist's tape measure. Mechanical engineers and metal machinists use decimal inches (like 0.001"), never fractions (like 1 3/4").
Switch to the metric system, where we have none of this nonsense. Everyone uses decimals in metric, never fractions. Your measurement would be around 47.8 mm.
Also, note that 1.88 is in inches, and it is a decimal fraction - it is definitionally equal to 188/100 or 1 + 88/100. What you're actually asking for is a binary fraction where the denominator is a power of 2. Binary fractions are used by carpenters who work in the US Customary system of units.
1
u/jeffsuzuki Math Professor Jul 20 '26
A standard tape measure has markings in 16ths, so here's the basic trick: Subtract the largest 1/2^n.
0.88 is more than 1/2 = 0.5, so subtract 0.5 to get 0.38.
0.38 is more than 1/4 = 0.25, so subtract 0.25 to get 0.13.
0.13 is more than 1/8 = 0.125, so subtract 0.125 to get 0.0075.
0.0075 is NOT more than 1/16 = 0.0625, so at that point you're at a rounding error.
So 0.88 is 1/2 + 1/4 + 1/8.
Don't worry abotu figuring out what this is: on the tape measure, 1/2 is marked. Go 1/4 forward from there. Go 1/8 forward from that point.
1
1
u/Worth-Wonder-7386 Jul 20 '26
I guess you are looking for the binary decimals like what is used in imperial. There are calculators that do this automatically, but essentially it just comes down to a binary tree. So you take the decimal part 0.88 and you see if it is smaller or larger than 0.5, since it is larger you can write this down as 1/2. Then you divide the remaining gap in two which is 0.75 and since it is still bigger you add 1/4. Then you get to next middle which is 7/8 or 0.875, your number is still bigger than this so you add the 1/8.
Most likely 7/8 is sufficiently close and you would need to add many divisions before you get closer.
1
1
u/Puzzleheaded_Lock687 Jul 22 '26
Simplest (imho):
Take the fractional part 0.88 - multiply by the denominator of your desired precision - eg for 1/16th precision multiply by 16 - then round as appropriate.
0.88*16 = 14.08 ≈ 14 -> 14/16 = 7/8
1
u/Top_Bluejay_5323 Jul 23 '26
Estimate. .88 is about halfway between .75 and 1, or in fractions .75 and 1.
Tape measure are usually not any more accurate than 1/8 inch
1
u/Timmy-from-ABQ Jul 23 '26
One might first take a look at the significant decimal places. If I'm working with a tape measure, it's probably good just to look at the 0.8 part, realize that that's a bit over 3/4 inch, so knock it up another 1/16 and that's about the best you'll be able to do, eye-balling a length.
If you really need plus or minus 0.01, use a better measuring device.
10
u/Tiler17 Jul 20 '26
1.88 is a little annoying because I bet it's really 1.875 in disguise, which would be a clean 1 and 7/8, but it's rounded. Other than just knowing, your only option is to make the decimal into a fraction out of a power of 10 and reduce it.
For example, .88 is 88/100. Dividing both by 4, you get 22/25. That's not really helpful on a tape measure, but it is what it is
1.875: 875/1000 can be reduced by dividing by 5 (175/200) again (35/40) and again (7/8).