How do you convert a decimal to a percent?

Percent means "per hundred". A decimal is a number written in tenths, hundredths and thousandths, and a percent is the same number with the hundredths column promoted to whole units. Converting between them does not change the quantity. It changes which column you are counting in, and that is why the whole job is one move of the decimal point.

Why it is exactly two places

Take 0.375. The digits sit in the tenths, hundredths and thousandths columns, so it is 375 thousandths. Thousandths are tenths of hundredths, so 375 of them make 37.5 hundredths. Thirty-seven and a half per hundred is 37.5%:

0.375  =  375/1000  =  37.5/100  =  37.5%

0.375 × 100  =  37.5           the same step, as arithmetic

Multiplying by 100 shifts every digit two columns to the left, which looks like the point sliding two places to the right. Either way of saying it gives the same digits. The point does not know which description you prefer.

The method, with the cases that catch people

Move the point two places right. When there are not enough digits, pad with zeros first, and when the decimal is above 1 let the percent go above 100:

0.375    →  37.5     =  37.5%
0.8      →  0.80     →  80       =  80%
0.5      →  0.50     →  50       =  50%      not 5%
0.04     →  4        =  4%       not 40%
0.125    →  12.5     =  12.5%
0.0025   →  0.25     =  0.25%
1.5      →  150      =  150%
2        →  2.00     →  200      =  200%
3.25     →  325      =  325%

Two of those rows do most of the damage. 0.5 has one digit after the point, so moving the point one place and stopping gives 5%, which is a tenth of the truth. Write the hidden zero, 0.50, and the point has room to travel. The other victim is 0.04, which turns into 40% when the leading zero gets counted as a digit worth keeping. It is not. 0.04 is four hundredths, and four hundredths is 4%.

The sanity check is one half. Anything under 0.5 must land under 50%, and anything over 1 must land over 100%. 0.04 is far below one half, so 40% was never a candidate.

Decimals above 1

A percent above 100 is not a mistake, it is a quantity above one whole. 1.5 is one and a half, so it is 100% plus 50%, which is 150%. If a shop's sales doubled, this year is 2.00 times last year, which is 200% of it. The percentage change post has more on what to do when a result lands above 100 and the headline writer panics.

Repeating decimals

The point moves two places and the repeating tail comes along for the ride. The tail does not stop just because it has been promoted:

0.333...    →  33.333...%   =  33 1/3%
0.666...    →  66.666...%   =  66 2/3%
0.1666...   →  16.666...%   =  16 2/3%
0.0833...   →   8.333...%   =  8 1/3%

The exact form on the right comes from writing the decimal as a fraction first. 0.333... is 1/3, and 1/3 of 100 is 100/3, which is 33 remainder 1, so 33 1/3%. The nines rule for turning the repeating decimal into that fraction lives in the repeating decimal post, and the fraction to percent post does the second half. For a headline, 33.33% is fine. For arithmetic that continues, keep the fraction, because 33.33% three times is 99.99%, and a third of something taken three times should be all of it.

Going back: percent to decimal

Divide by 100. The point moves two places to the left, and now the padding zeros go on the front:

45%     →  0.45
7%      →  0.07      =  0.07     not 0.7
5%      →  0.05
150%    →  1.5
100%    →  1
12.5%   →  0.125
0.5%    →  0.005
250%    →  2.5

The mirror image of the 0.5 trap is 5%. It has one digit, so one move of the point gives 0.5, which is 50% and ten times too big. Write 05, then move: 0.05. A percent under 10 always starts 0.0 as a decimal, and a percent under 1 always starts 0.00.

Where you actually need the decimal

The reason this conversion matters is that you cannot multiply by a percent. "20% of 48.60" is really 48.60 × 0.20, and the 0.20 is the percent after the point has moved two places left:

20% tip on 48.60      48.60 × 0.20   =  9.72
8% tax on 250         250 × 0.08     =  20
35% off 80            80 × 0.35      =  28     80 − 28  =  52
                      80 × 0.65      =  52          one step, 100% − 35% = 65%

The discount row shows the shortcut. Paying 35% less means paying 65%, and 65% is 0.65, so one multiplication gets you to the price. The tip post and the discount post use this constantly without saying so.

Interest rates work the same way. The simple interest formula is I = P × r × t, and r is the rate as a decimal, so 4% goes in as 0.04. For 5,000 at 4% for 3 years that is 5,000 × 0.04 × 3 = 600. Type 4 instead of 0.04 and the formula hands back 60,000, which is a very different bank. The simple interest post has the rest.

The conversions worth knowing by heart

The third column is there because the three notations are one number in three outfits. Any decimal can be read as a fraction over a power of ten and reduced, which the decimal to fraction post covers, and any fraction can be read as a percent by scaling the denominator to 100. If the decimal is a measured result rather than a tidy one, the percentage post starts from the raw part and whole instead.

Where a calculator gets this wrong

Moving a decimal point is the one operation that should be impossible to get wrong, and most software manages it anyway. Numbers are stored in binary floating point, and most decimals have no exact binary form, so 0.07 is stored as the nearest binary fraction. Multiply that by 100 and the error surfaces. These are real results from JavaScript and Python:

0.07 × 100     =  7.000000000000001      should be 7
0.57 × 100     =  56.99999999999999      should be 57
0.29 × 100     =  28.999999999999996     should be 29
1.1  × 100     =  110.00000000000001     should be 110
0.07 × 100 == 7                          False

Seven hundredths is 7%. Not 7 and a quadrillionth, and not a value that a program refuses to recognise as 7. It is the same fault that makes 0.1 + 0.2 miss 0.3, and the usual patch is to round the display and hope nobody compares. Prism does the arithmetic on exact decimals instead, so 0.07 × 100 is 7, 0.1 + 0.2 is exactly 0.3, and a percent you typed is the percent you get back.

Type 0.375 × 100 and read 37.5

Prism computes exactly, so 0.07 × 100 comes back as 7, not 7.000000000000001. When you have a part and a whole instead of a decimal, the percentages tool takes the Part and the Whole and shows the Share. Percentages, fractions and the scientific mode are free forever, no ads, no subscription. See the app.