Equivalent Decimals: Useful Fractions As Decimals

equivalent decimalsLooking for a list of equivalent decimals — common or useful fractions shown in their decimal form? Below are some of the most important ones, along with a bit of background information on decimal numbers.

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Decimal Numbers Made Very Easy

First, some background on decimal numbers, in case you’re a bit rusty on the subject.

Non-decimal numbers (i.e., whole numbers, or, in proper mathematical terminology, integers) are pretty simple: every time you move one place to the left, you multiply by 10. So 1,000 is 10 times 100, which is 10 times 10, which is 10 times 1. With decimal numbers, you do the same thing, except that you move to the right, and you divide by 10 each step of the way, so 0.1 is 1 divided by 10, 0.01 is 0.1 divided by 10, 0.001 is 0.01 divided by 10, etc.

That already gives you the first set of decimal equivalents:

1/10 = 0.1         1/10,000 = 0.0001
1/100 = 0.01       1/100,000 = 0.00001
1/1,000 = 0.001    1/1,000,000 = 0.000001

What About That Leading Zero?

Notice something? We always start decimal numbers with a 0 just before the decimal point. You don’t need to do this, because it doesn’t actually change the value of the number, but it does make it easier to see that there’s a decimal point. Otherwise, it’s too easy to overlook the decimal point.

If there’s already a number to the left of the decimal point, you don’t need to add anything, so 1.75 is fine just the way it is, since it’s easy to see the decimal. But look at the difference between just plain .75 and 0.75 — with .75, it’s too easy to miss the decimal under less-than-favorable conditions.

So the leading 0 is really just a matter of style, but it’s good style, so we’ll use it here.

Some Basic Fractions

OK. Let’s get down to fractions. Here are some basic fractions that come up frequently in measurements of all kinds, and which often show up in making change, calculating interest, and other business situations:

1/2 = 0.5      3/8 = 0.375      13/16 = 0.8125
1/4 = 0.25     5/8 = 0.625      15/16 = 0.9375
3/4 = 0.75     7/8 = 0.875      1/25 = 0.04
1/5 = 0.2      1/16 = 0.0625    1/32 = 0.03125
2/5 = 0.4      3/16 = 0.1875    1/64 = 0.015625
3/5 = 0.6      5/16 = 0.3125    1/128 = 0.0078125
4/5 = 0.8      9/16 = 0.5625    1/256 = 0.00390625
1/8 = 0.125    11/16 = 0.6875

If you can remember at least the first three or four of those, you’ll find that they come in handy in a lot of situations. Let’s take a moment to look at how you would put common decimal fractions to use:

Fractions On The Fly

Most mobile phones and similar device have at least some kind of built-in calculator, and if you already know the decimal equivalents of common fractions, you can quickly use them to figure out, for example, what the actual sale price of an item is when it’s marked down by a fraction. let’s say that a $5.95 item is on sale for 1/4 off. If you know that 1/4 is 0.25, you can enter the price in the calculator, multiply it by 0.25, and find out the sale price:

  5.95
x 0.25
--------
  1.4875

That rounds up to $1.49, so you subtract $1.49 from $5.95 to get the actual sale price.

if you know the decimal equivalent of 3/4, you can eliminate the subtraction: since 1 – 1/4 = 3/4, you know that the actual sale price is going to be 3/4 of $5.95:

  5.95
x 0.75
-------
 4.4625

Round it down to the nearest cent, and you have the sale price: $4.46.

Not-So-Easy Fractions

There are fractions that don’t behave so nicely when you turn them into decimals: they just seem to keep going on forever (and in fact, many of them do just that). What can you do with a fraction like this, for example?

1/3 = 0.33333333333333333333333333333333333...

It does go on forever! (That’s what the three dots at the end are for – to show that it’s an endless decimal.) So how do you use it?

The further right you go, the smaller the numbers get, because you’re dividing by 10 every time you take a step to the right. So once you go more than a few places to the right, those 3s shrink away to almost nothing, and you can just cut them off. The difference between 0.33333 and 0.333333, for example, is 3/1,000,000, or three millionths. If somebody offers you the choice between $1,000,000.00 and $1,000,003.00, you probably aren’t going to worry too much about the difference.

So basically, when you see an endless decimal fraction, you round it off at some convenient point, and just use the part that you do need.

The Odd Ones, And Then Some

Here are some common fractions that turn into endless decimals:

1/3 = 0.33333333333...     1/9 = 0.11111111111...
2/3 = 0.66666666666...     1/11 = 0.0909090909...
1/6 = 0.16666666666...     1/12 = 0.08333333333...
5/6 = 0.83333333333...     1/13 = 0.07692307692...
1/7 = 0.14285714285...

A Few Tricks

There are far too many (as in an infinite number of) fractions to list here, but as long as you have access to some kind of calculator (or a pencil and paper, and a lot of time and patience) there are a few tricks that make working with fractions in decimal format a lot easier.

Multiply

First, if you know what the decimal version of a fraction is, you can always calculate other fractions with the same numerator or denominator just by multiplying or dividing:

1/7 = 0.14285714285...
so
3/7 = 3 x 0.14285714285...
or
0.42857142855...

Convert

Second, you can convert any fraction to a decimal using a calculator by entering the numerator (the number on top) first, then dividing it by the denominator. The result will be the decimal version of the fraction. Take a moment to try it with a calculator:

27/133 = 0.2030075187969...

In The Ballpark

Third, if all you need is a ballpark number, and you know a decimal fraction that’s close to the one you want, with a little practice, you can make some smart guesses. For example, 32/53 is pretty close to 30/50, which is just 3/5, which is 0.6, so if you use 0.6 for 32/53, you won’t be very far from the mark (in fact, you’ll miss it by only about 1/250, or 0.004).

If you know some basic math, you’re ahead of the game, and knowing advanced math can be a major advantage. Whether it’s basic household accounting, business, finance, or engineering, there are online arithmetic and mathematics courses to suit your needs.