Fractions, decimals, and percentages

A single TEAS question can hand you a dose as a fraction, ask for the answer as a decimal, and expect you to sanity check it as a percentage. The three forms are one quantity written three ways, so what is actually being tested is whether you can move between them without stopping to work out which one you are looking at.

What each form actually says

A fraction such as 3/8 states a part over a whole. The denominator, 8, is how many equal pieces make up the whole, and the numerator, 3, is how many of those pieces you have. A decimal puts that same value on a base-ten scale, so 0.375 reads as three hundred seventy-five thousandths. A percentage restates it out of 100, so 37.5% means 37.5 for every hundred.

None of the three is more correct than the others. The exam picks whichever form makes the question slower to read, which is why the conversion has to be automatic rather than something you reason out under the clock.

Rational number. Any value that can be written as one whole number over another, which covers every fraction, every terminating decimal, and every percentage you will meet on the exam.

The four conversions

Four moves cover everything the TEAS asks. The table runs one value all the way around the loop, so you can see the same quantity in all three forms.

Going from	To	What you do	Worked through
Fraction	Decimal	Divide the numerator by the denominator	5/8 becomes 0.625
Decimal	Percentage	Multiply by 100, moving the point two places right	0.625 becomes 62.5%
Percentage	Decimal	Divide by 100, moving the point two places left	62.5% becomes 0.625
Decimal	Fraction	Digits over the matching power of ten, then simplify	0.625 becomes 625/1,000, then 5/8

Fraction to decimal is a long division

A fraction bar is a division sign. The numerator goes inside the bracket, the denominator goes outside, and you add a decimal point and as many zeros as you need after the numerator.

Some fractions never reach a remainder of zero. Carry those to the thousandths place, then round back to the hundredths on the usual rule: if the thousandths digit is 5 or more, round the hundredths digit up, and if it is below 5, leave it alone.

Decimal to fraction, then simplify

Read the place value of the last digit, put the digits over that power of ten, and reduce. A decimal ending in the hundredths goes over 100, one ending in the thousandths goes over 1,000, and so on.

A percentage that already contains a decimal takes one extra step, since you have to clear that decimal before you can simplify.

Reading decimal place value

Every digit after the point has a name: tenths, hundredths, thousandths, ten-thousandths, hundred-thousandths. Read the value from its last nonzero digit. In 0.00036 the 6 sits in the hundred-thousandths place, so the whole value is thirty-six hundred-thousandths.

This carries more weight than it looks. Rounding questions and comparison questions both turn on place value, and misreading a place by one shifts the value by a factor of ten, which on a dosage question is the difference between a plausible answer and an impossible one.

The three forms are not three topics. They are one quantity, and the exam is testing how quickly you can change its clothes.

Practise the loop in the table until you can run a value from fraction to decimal to percentage and back without notes. Then move on to operations with rational numbers, where all three forms start turning up inside the same expression.