Arithmetic and Estimation

You’re at a restaurant and the bill comes to $47.83. You want to leave a 20% tip. You don’t pull out a calculator — you round $47.83 to $48, take 10% ($4.80), double it ($9.60). Done in three seconds.

That same skill — rounding to friendly numbers and building from simple pieces — is exactly what the MCAT rewards. You won’t have a calculator during the physics, chemistry, or biochem sections. Good mental-math habits are worth many minutes over the course of a test. This section teaches the tricks that matter most.

The 10% Trick

The single most useful mental math tool: to find 10% of any number, just move the decimal point one place to the left.

• 10% of 250 = 25
• 10% of 7.4 = 0.74
• 10% of 0.036 = 0.0036

Once you have 10%, you can build any common percentage:

Example: What is 15% of 320?

• 10% of 320 = 32
• 5% of 320 = 16 (half of 32)
• 15% of 320 = 32 + 16 = 48

Rounding to “Nice” Numbers

When a problem gives you 4.87 x 3.12, do not try to compute this exactly. Round to 5 x 3 = 15. The actual answer is 15.19. You were off by about 1%, and it took you two seconds instead of thirty.

The key principle: round each number to one significant figure (the first non-zero digit), then do simple arithmetic.

• 6.02 x $10^{23}$ becomes 6 x $10^{23}$
• 1.38 x $10^{-23}$ becomes 1.4 x $10^{-23}$
• 9.8 m/s² becomes 10 m/s²

Multiplication Shortcuts

Multiplying by 0.5 = dividing by 2 (halving). If something costs half as much energy, just divide by 2.

Multiplying by 2 = doubling. Obvious, but students sometimes overcomplicate. If a drug dose doubles, the concentration doubles.

Multiplying by 5 = multiply by 10 then halve. So 5 x 37 = $\frac{370}{2}$ = 185.

Squaring numbers ending in 5: Take the number before the 5, multiply by the next number up, and tack 25 onto the end. For example, $35^{2}$ — take 3, multiply by 4 = 12, then tack on 25 → 1225. Or $65^{2}$ — take 6 × 7 = 42, then 4225.

Division Shortcuts

Dividing by 2 = multiplying by 0.5 (halving).

Dividing by 5 = multiply by 2 then divide by 10. So $\frac{430}{5}$ = $\frac{860}{10}$ = 86.

Dividing by 3 - know that $\frac{1}{3}$ = 0.333. So $\frac{90}{3}$ = 30, $\frac{100}{3}$ = 33.3.

Dividing by large numbers - convert to scientific notation first. For example: $\frac{6000}{200}$ = (6 x $10^{3}$)/(2 x $10^{2}$) = 3 x $10^{1}$ = 30.

Common Fractions You Should Know Cold

Knowing these by heart lets you instantly convert between fractions, decimals, and percentages during a passage.

When to Estimate vs. When to Calculate

Estimate when the answer choices are spread apart (e.g., 12, 24, 48, 96). Calculate more carefully when the choices are close together (e.g., 3.2, 3.6, 4.0, 4.4). On most MCAT questions, estimation is sufficient - the test makers deliberately space answer choices to reward good estimation.