On the test
Problem-Solving and Data Analysis is about 15% of the Math section, around 2 to 4 questions in each 22-question module, spread through the module from easier to harder.
5 to 7 of the 44 questions (about 2 to 4 in each module). Spread through the module, easier first and harder at the end.
How I approached it
A small story from Aime
When I face a unit conversion, I think about changing money at the exchange counter. The money is still the same value, only the name on the notes has changed. Nobody becomes richer at the counter. So the first thing I ask is whether I am going from a big unit to a small unit. If I go from dollars to francs, I should get a big pile of francs. If I come back, I get a small number. I also keep the names with the numbers, so I can see which name cancels. The same thinking works for meters and kilometers, minutes and hours, or liters and cubic meters. On the SAT, I use the conversion fact, cancel the units, and check that the size makes sense.
Unit questions look long, but the idea is small: same amount, different name. Take one unit at a time and you will not get lost.
What is inside this part
One given fact changes the unit once.
Hours to minutes · Kilometers to meters · Inches to centimeters
A chain of two or more facts to reach the wanted unit.
Days to seconds · Liters to cubic meters to hours
Changing both units of a rate, such as km/h to m/s.
Speed · Price per gram to price per kilogram · Flow rates
Conversions where the factor must be squared or cubed.
Square meters to square centimeters · Cubic meters to liters
How to know a question is from this part
The numbers are in one unit, and the answer must be in another unit.
- A conversion fact in the question, like 1 inch = 2.54 centimeters
- Two different units in the same sentence
- Phrases like how many centimeters, in meters per second, in square units
- A rate with a changed unit, such as km/h in the question and m/s in the answer
- Area or volume (square or cubic) with a length conversion
The lesson
1. What a unit conversion is
A unit is the name that tells what you are counting, like meters, hours, liters or RWF. Unit conversion means writing the same amount with a different unit.
2 hours and 120 minutes are exactly the same time. Only the unit is different. The SAT will give you the conversion fact (like 1 mile = 1.6 kilometers) in the question. You do not need to memorize hard ones, but know the easy ones: 60 minutes in an hour, 100 cm in a meter, 1,000 m in a kilometer, 1,000 g in a kilogram, 1,000 mL in a liter.
2. Big unit or small unit?
Before calculating, decide: am I going from a big unit to a small unit, or from small to big? A kilometer is big and a meter is small. It takes 1,000 small meters to make 1 big kilometer.
Big to small: the number gets bigger (multiply). Small to big: the number gets smaller (divide). This one idea catches most mistakes.
3. The cancel method
Write the conversion as a fraction that equals 1. For example, 1,000 m / 1 km = 1 because they are the same length. Multiply your amount by the fraction so that the unit you do not want cancels out.
To change 3.4 km to meters: 3.4 km × (1,000 m / 1 km). The km on top and bottom cancel. What remains is 3.4 × 1,000 = 3,400 m.
4. Worked example 1: one step
Let us start simply.
One inch equals 2.54 centimeters. How many centimeters are in 12 inches?
Show the steps
- Inches to centimeters: big unit to small unit, so the number gets bigger.
- 12 × 2.54 = 30.48.
- Check: 30.48 is bigger than 12. Good.
30.48 centimeters
5. Multi-step conversions
Sometimes you need two or three conversions in a chain. Do them one at a time, and keep the units. For example, days to seconds goes days to hours to minutes to seconds. One day is 24 × 60 × 60 = 86,400 seconds.
Do not rush. Write the units after every number, and let them cancel step by step.
6. Worked example 2: converting a rate
A rate has two units, so you may convert both of them. Convert the top unit and the bottom unit separately.
A train goes 72 kilometers per hour. What is its speed in meters per second?
Show the steps
- Kilometers to meters: 72 × 1,000 = 72,000 m.
- Hours to seconds: 1 hour = 3,600 seconds.
- 72,000 ÷ 3,600 = 20.
- Check with the shortcut: divide km/h by 3.6 to get m/s. 72 ÷ 3.6 = 20.
20 meters per second
7. Area and volume units
Careful: for area and volume, the conversion number is squared or cubed. If 1 m = 100 cm, then 1 square meter is 100 × 100 = 10,000 square centimeters. And 1 cubic meter is 100 × 100 × 100 = 1,000,000 cubic centimeters.
The easiest safe method is to convert the side lengths first, then find the area or volume with the new units.
8. Worked example 3: area
Convert the sides first.
A square garden has sides of 3 meters. What is its area in square centimeters? (1 meter = 100 centimeters)
Show the steps
- Each side: 3 m = 300 cm.
- Area = 300 × 300 = 90,000 square centimeters.
- Wrong way: 9 × 100 = 900, because it does not square the 100.
90,000 square centimeters
9. Common traps
Trap 1: multiplying when you should divide, and the other way round. Use the big and small check.
Trap 2: forgetting to square or cube the factor for area and volume.
Trap 3: doing only half of a rate conversion, such as km/h to m/h.
Trap 4: stopping at a middle unit, like liters, when the question asks for cubic meters.
Trap 5: not reading which unit the last sentence wants.
See it
Going to the smaller unit gives a bigger number. Going to the bigger unit gives a smaller number.
| Fact | Use it for |
|---|---|
| 60 seconds = 1 minute | Time |
| 60 minutes = 1 hour | Time |
| 24 hours = 1 day | Time |
| 100 cm = 1 m | Length |
| 1,000 m = 1 km | Length |
| 1,000 g = 1 kg | Mass |
| 1,000 L = 1 cubic meter | Volume |
- 1Write the amount with its unit
- 2Choose the big or small direction
- 3Multiply by a fraction that cancels the old unit
- 4Repeat until you reach the unit the last sentence asks for
Videos that can help
Ask in the community. Tutors and other students answer.
Ask a question