GMAT Decimals From Scratch
Decimals show up on the GMAT wrapped in notation that looks harder than it is. Most of the difficulty comes from three places: knowing which digit is which, moving the decimal point correctly, and rounding to the right place. None of it is hard maths, and all of it is easy to get wrong under time pressure.
A digit and a decimal are different things
A digit is a single symbol, 0 through 9. The number 375 is made of three digits.
A decimal is a number with a whole part and a fractional part, like 3.75. Worth knowing: every whole number can be written as a decimal. 5, 5.0, and 5.00 are the same value. Whole numbers are part of the decimal family, not separate from it.
Learn the digit names, and watch the gap
Left of the decimal point the names end in s: ones, tens, hundreds, thousands. Right of it they end in ths: tenths, hundredths, thousandths.
The trap is that there is no "oneth". The sequence on the right starts at tenths. Counting places as if a units position existed on the right is a common source of rounding errors.
For continental European readers there is a second trap. In the UK and US the comma separates groups of three digits and the point separates whole from fractional. In 3,725.48 the comma and the point are doing different jobs.
Multiplying by powers of 10 just moves the point
Count the zeros, move the decimal point that many places. Right for multiplication, left for division.
4.67 × 100 becomes 467. Two zeros, two places right. 56.8 ÷ 1,000 becomes 0.0568. Three zeros, three places left, with a zero added at the front because the number runs out.
This is worth making automatic. It appears constantly, often disguised inside a larger calculation.
Rounding is a three-step check
Identify the digit you are rounding to. Look at the digit immediately after it. If that next digit is 5 or above, round up; 4 or below, round down.
Round 5.678 to the nearest tenth: the tenths digit is 6, the next digit is 7, so round up to 5.7. Round 12.8341 to the nearest hundredth: the hundredths digit is 3, the next is 4, so round down to 12.83.
The mistake to avoid is looking at more than one following digit, or at the last digit in the number rather than the next one.
Scientific notation is just a power of 10
You do not need the name for the GMAT, and you will meet the notation. 5,280,000 written as 5.28 × 10⁶, or 0.000072 as 7.2 × 10⁻⁵.
Treat the power of 10 as an instruction about where to move the decimal point. A negative exponent moves it left, so 1.8766 × 10⁻¹ is 0.18766.
You probably do not need long division
Nine times out of ten, when a GMAT question looks like it needs long division, it does not. There is usually a simplification or an approximation that gets there faster.
It is still worth being able to do it, since the tenth case exists. Use whichever layout you learned at school. The cycle is the same everywhere: divide, multiply, subtract, bring down, repeat.