SAT grid-in rules, units, and percents

What a grid-in looks like

In each Math , a few questions have no answer choices. You type your answer in a box instead, and these are called . Under the box, an Answer Preview shows what you typed, with a fraction drawn stacked. The entry rules are listed on the left side of the screen, the same on every grid-in, so learn them now and skip them on test day.

With choices, a wrong setup often gives a number that isn't in the list, and that sends you back to the question. A box takes whatever you type. You have to check for yourself that your number is what the last line asks for, and that it's in a form the box accepts.

The math itself is taught in the ratios and units lesson and the percentages lesson. This one is about getting your answer into the box.

Working one grid-in

A pump moves 9 quarts of water per minute. How many hours does it take the pump to move 250 gallons? (1 gallon = 4 quarts)

The last line asks for hours, so write "hours" at the top of your scratch paper. You're given gallons and quarts per minute, so the units have to change more than once. Write the unit on every number and let them cancel.

Gallons cancel, leaving quarts.
$250\text{ gal}\times\frac{4\text{ qt}}{1\text{ gal}}=1{,}000\text{ qt}$
Quarts cancel, leaving minutes.
$1{,}000\text{ qt}\times\frac{1\text{ min}}{9\text{ qt}}=\frac{1{,}000}{9}\text{ min}$
Minutes cancel, leaving hours.
$\frac{1{,}000}{9}\text{ min}\times\frac{1\text{ hr}}{60\text{ min}}=\frac{1{,}000}{540}\text{ hr}$
Divide the top and bottom by 20.
$\frac{1{,}000}{540}=\frac{50}{27}$

Partway through, you had $\frac{1{,}000}{9}$ , about 111.1. That's the time in minutes, and it looks like a finished answer. The question asked for hours, so keep going until the unit on your last line matches the one at the top of your paper.

Now type it. 1000/540 needs 8 characters, and the box holds 5. 50/27 fits and it's exact, so type that. If you'd rather use a decimal, 50/27 is 1.85185..., so type 1.851 or 1.852.

The Answer Preview should show 50/27 as a stacked fraction. Then read the last line once more. It asks for hours, and 50/27 is in hours.

When the units change

A unit question asks for a unit its numbers aren't in, like "in square feet", and often hands you the conversion fact in parentheses. Set up each fact as a fraction with the unit you're getting rid of on the bottom, as in the pump question. After each step, ask whether the number should get bigger or smaller. An hour is longer than a minute, so 111.1 minutes had to become fewer hours.

For square units, square the conversion factor. For cubic units, cube it.

Right: 5 ft² = 5 × 12² = 720 in²
Wrong: 5 ft² = 5 × 12 = 60 in²

A square foot is 12 inches on each side, so the factor gets used once for each side.

A rate like square feet per hour has two units. Change them one at a time, and stop only when both match the question.

Worked example

A saddlery sorts leather scraps at a constant rate of 510 square feet per hour.

Which is closest to this rate in square meters per minute? (Use $1$ meter $= 3.28$ feet.)

A
$2.59$
B
$47.40$
C
$0.79$
D
$91.45$

Show the answer

A
$2.59$
You get $2.59$ by dividing $510$ by $3.28$ once and then by $60$ . This uses a linear conversion factor for square units; converting square feet to square meters requires dividing by $3.28^2$ .
B
$47.40$
Dividing $510$ by $3.28^2$ gives about $47.40$ square meters per hour. This leaves the time unit in hours, so you still need to divide by $60$ to get the rate per minute.
C
$0.79$
Correct answer
Since $1$ square meter equals $3.28^2$ square feet, divide $510$ by $3.28^2$ to convert the area units. Then divide by $60$ to convert the hourly rate to a per-minute rate, giving $510 \div 3.28^2 \div 60 \approx 0.79$ square meters per minute.
D
$91.45$
You get $91.45$ by multiplying $510$ by $3.28^2$ and then dividing by $60$ . This reverses the area conversion: each square meter contains $3.28^2$ square feet, so converting square feet to square meters requires division.

Solution

Square the length conversion factor to convert area: $1$ square meter equals $3.28^2 = 10.7584$ square feet. The rate in square meters per hour is therefore $\frac{510}{10.7584}$ .

An hour has $60$ minutes, so divide the hourly rate by $60$ : $\frac{510}{10.7584 \times 60} \approx 0.79008$ square meters per minute. The closest listed value is $0.79$ .

Report a problem

When a percent changes

Turn each percent into a multiplier before you calculate. Up 40% is $\times1.40$ , and down 15% is $\times0.85$ . If the question gives no starting amount, start at 100. Say a price goes up 40% and then down 15%, and the question asks for the overall percent increase.

Up 40%.
$100\times1.40=140$
Down 15%, taken of the new price, 140.
$140\times0.85=119$
The increase, out of the starting 100.
$119-100=19$

That's a 19% increase, so type 19. In Desmos, 100*1.4*0.85 gives 119 on one line.

To undo a change, divide by its multiplier. A price of $68 after 15% off started at $68\div0.85=80$ , not $68\times1.15$ . Percentages has more.

Trap: The final amount typed as the change

119 is the final price as a percent of the original. It's the last number in your work, so it's the easy one to type, but the price went up by 19%.

What to do: Subtract the starting 100 before you type. Then reread the last line: does it ask for the new amount as a percent of the old one, or for the percent change?

The box can't take a percent sign, so the question decides what your number means. Say a quarter of a club's members are seniors.

For a percent question, type the percent as a plain number.

Right: What percent of the members are seniors? Type 25.
Wrong: What percent of the members are seniors? Type .25.

.25 is scored as 0.25 percent, a hundred times too small.

A runs from 0 to 1, so the probability that a member picked at random is a senior goes in as .25 or 1/4.

Worked example

A positive number is decreased by $24\%$ . The resulting number is $125\%$ of a positive number $y$ .

The number $y$ is what percent less than the original positive number?

A
$39.2\%$
B
$43\%$
C
$44\%$
D
$49\%$

Show the answer

A
$39.2\%$
Correct answer
Let the original number be $100$ . After a $24\%$ decrease, it is $76$ . Since $76$ is $125\%$ of $y$ , $y=76\div1.25=60.8$ , which is $39.2\%$ less than $100$ .
B
$43\%$
This treats $y$ as $25\%$ less than the changed number, reversing the direction of the relationship. Because the changed number is $125\%$ of $y$ , you must divide $76$ by $1.25$ .
C
$44\%$
This subtracts $20\%$ of the original number from $76$ . Since $y$ is $80\%$ of the changed number, the $20\%$ reduction must be calculated from $76$ , not $100$ .
D
$49\%$
This adds the $24\%$ decrease and an apparent $25\%$ decrease. The relationships apply to different bases, so their percentages cannot be added.

Solution

Let the original positive number be $100$ . Decreasing it by $24\%$ gives

$100(1-0.24)=76$ . The resulting number is $125\%$ of $y$ , so

$76=1.25y$ and

$y=\frac{76}{1.25}=60.8$ . The percent by which $y$ is less than the original number is

$\frac{100-60.8}{100}\times100\%=39.2\%$ .

Report a problem

What the box accepts

The box takes digits, one decimal point or one slash, and a minus sign at the start. A positive answer can use 5 characters and a negative answer 6, so the minus sign doesn't cost you a digit.

The box drops anything else as you type, so $1,200 lands as 1200. Leave the symbols out anyway and check what the box shows, because a dropped comma or space can push two numbers together. Say a question asks for one possible value of $x$ , and you find that $x=3$ or $x=8$ .

When more than one value works, type just one of them.

Right: Type 3, or type 8.
Wrong: Type 3,8.

The comma is dropped, so the box shows 38, which isn't either answer.

Fractions and decimals that don't fit

A fraction doesn't have to be reduced. If your work ends at 6/8, type 6/8. Type the fraction whenever it fits. If fractions are where you tend to slip, type the decimal every time instead, and fill all five characters when it runs long.

Some fractions are too long and can't be reduced, like $\frac{263}{40}$ , which has six characters.

If a fraction doesn't fit, type its decimal.

Right: 6.575
Wrong: 263/4

The box stops at five characters, so the 0 never goes in, and 263/4 is 65.75.

For an answer of $2\frac{3}{4}$ :

Change a mixed number to a fraction or a decimal before you type it.

Right: 11/4 or 2.75
Wrong: 2 3/4

The space is dropped, so the box shows 23/4, which is 5.75.

A decimal that keeps going can be cut off at the last character or rounded there, and either way it scores. For $\frac{7}{9}=0.7777\ldots$ :

When a decimal keeps going, fill all five characters.

Right: .7777, .7778, 0.777 or 0.778
Wrong: .78 or 0.78

.78 is scored as the number 0.78, and that isn't 7/9. Only an entry that fills all five characters counts as close enough.

The 0 in front is optional, and leaving it out makes room for one more digit. 0.7777 has six characters, so the last 7 never goes in.

A negative answer works the same way, with one more character for the minus sign. For $-\frac{5}{6}=-0.8333\ldots$ , type -5/6, -.8333 or -0.833. -.83 stops too soon.

Worked example

Over a single maintenance shift, Nakagawa Wind Farm recorded a total of $3{,}280$ minutes of service across $8$ turbines.

What was the average service time, in hours per turbine?

Show the answer

Accepted answers: 41/6, 6.833

Solution

Divide the total service time by $8$ turbines:

$\frac{3{,}280}{8}=410$ minutes per turbine. Convert minutes to hours by dividing by $60$ :

$\frac{410}{60}=\frac{41}{6}=6.8333\ldots$ hours per turbine. A common wrong answer is $410$ , which divides by the number of turbines but leaves the average in minutes. Another common wrong answer is $24{,}600$ , which multiplies $410$ by $60$ instead of dividing by $60$ to convert minutes to hours.

Note that $41/6$ and $6.833$ are examples of ways to enter a correct answer.

Report a problem

When time is running out

A blank grid-in scores the same as a wrong one. With 2:00 left in the module, type your best number in every empty box, starting from whatever work you have. If you'd gotten as far as 111.1 minutes on the pump question, dividing by 60 takes a few seconds and might earn the point.

Practice

Before you start each question, say the unit the last line asks for. On a grid-in, read the Answer Preview before you move on.

Try it

5 questions on this skill, with every choice explained.

Start the drill

Next steps

Drill this in five questions

Drills need a free account, which also saves your lesson progress on every device. Sign up free

Related lessons

Units, percents, and grid-in entry rules

What a grid-in looks like

Working one grid-in

When the units change

When a percent changes

What the box accepts

Fractions and decimals that don't fit

When time is running out

Practice