Science You're Expected to Know · Lesson 1

Units, prefixes and scientific notation

ACT’s description of the Science section says advanced knowledge isn’t required, but background from introductory science courses can help on some questions. This module covers that background one subject at a time, and always inside a data passage, because that is where you’ll use it.

Start with measurement. A metric prefix multiplies the base unit: kilo- (k) means 1,000, centi- (c) means 1/100, milli- (m) means 1/1,000 and micro- (µ) means 1/1,000,000. So 1 km = 1,000 m, 1 m = 100 cm = 1,000 mm, 1 mm = 1,000 µm, and 1 L = 1,000 mL.

To compare values written in different units, rewrite them in one unit first. Moving to a smaller unit makes the number bigger (0.04 cm = 0.4 mm); moving to a bigger unit makes it smaller (150 µm = 0.15 mm). A big number in a small unit can still be the smaller amount.

Scientific notation writes a number as a value from 1 to 10 times a power of ten. Compare the exponents first: with negative exponents, the one closer to zero is bigger, so 2 × 10⁻³ (0.002) is larger than 3 × 10⁻⁴ (0.0003) even though 3 is larger than 2. To divide powers of ten, subtract the exponents: 10⁻² ÷ 10⁻⁴ = 10².

Prefixes you can expect
PrefixMeansExample
kilo- (k)× 1,0002.5 km = 2,500 m
centi- (c)× 1/1000.04 cm = 0.4 mm
milli- (m)× 1/1,000500 mL = 0.5 L
micro- (µ)× 1/1,000,000150 µm = 0.15 mm

Sediment in a Stream

Students filled one 500 mL bottle with stream water and sediment at each of four sites, Sites 1 to 4. For each site they recorded the typical diameter of the sediment grains in whatever metric unit their measuring tool showed, the mass of one typical grain, the dry mass of all the sediment in the bottle, and the time a typical grain took to sink through 50 cm of still water (Table 1).

Table 1
SiteTypical grain diameterMass of one grain (g)Sediment in bottle (g)Time to sink 50 cm (s)
Site 12 mm1 × 10⁻²2.53
Site 20.5 mm2 × 10⁻⁴4.09
Site 3150 µm5 × 10⁻⁶1.540
Site 40.04 cm9 × 10⁻⁵3.012
For Sites 1 to 4: typical grain diameter 2 mm, 0.5 mm, 150 µm and 0.04 cm; mass of one grain 1 × 10⁻², 2 × 10⁻⁴, 5 × 10⁻⁶ and 9 × 10⁻⁵ g; sediment in the 500 mL bottle 2.5, 4.0, 1.5 and 3.0 g; time to sink 50 cm 3, 9, 40 and 12 s. Larger grains are heavier and sink faster.

Worked example Easy

Show the whole passage

Sediment in a Stream

Students filled one 500 mL bottle with stream water and sediment at each of four sites, Sites 1 to 4. For each site they recorded the typical diameter of the sediment grains in whatever metric unit their measuring tool showed, the mass of one typical grain, the dry mass of all the sediment in the bottle, and the time a typical grain took to sink through 50 cm of still water (Table 1).

Table 1
SiteTypical grain diameterMass of one grain (g)Sediment in bottle (g)Time to sink 50 cm (s)
Site 12 mm1 × 10⁻²2.53
Site 20.5 mm2 × 10⁻⁴4.09
Site 3150 µm5 × 10⁻⁶1.540
Site 40.04 cm9 × 10⁻⁵3.012
For Sites 1 to 4: typical grain diameter 2 mm, 0.5 mm, 150 µm and 0.04 cm; mass of one grain 1 × 10⁻², 2 × 10⁻⁴, 5 × 10⁻⁶ and 9 × 10⁻⁵ g; sediment in the 500 mL bottle 2.5, 4.0, 1.5 and 3.0 g; time to sink 50 cm 3, 9, 40 and 12 s. Larger grains are heavier and sink faster.

According to Table 1, the typical grain diameter at Site 4, written in millimeters, is:

  1. 0.004 mm
  2. 0.04 mm
  3. 0.4 mmAnswer
  4. 4 mm

How to solve it

  1. From the passage: Table 1, Site 4 row, diameter column: 0.04 cm.
  2. From background: 1 cm = 10 mm. Going to a smaller unit makes the number bigger.
  3. 0.04 × 10 = 0.4, so the diameter is 0.4 mm.

Why each choice is right or wrong

  • A. Incorrect. 0.004 mm divides by 10 instead of multiplying. Millimeters are smaller than centimeters, so the number must get bigger.
  • B. Incorrect. 0.04 mm copies the number from Table 1 and changes only the unit. A centimeter is 10 mm, so the number has to change too.
  • C. Correct. Table 1 gives 0.04 cm for Site 4 (passage). From background, 1 cm = 10 mm, so 0.04 cm × 10 = 0.4 mm.
  • D. Incorrect. 4 mm multiplies by 100, as if 1 cm were 100 mm. It is 1 m that equals 100 cm; 1 cm is only 10 mm.

Worked example Medium

Show the whole passage

Sediment in a Stream

Students filled one 500 mL bottle with stream water and sediment at each of four sites, Sites 1 to 4. For each site they recorded the typical diameter of the sediment grains in whatever metric unit their measuring tool showed, the mass of one typical grain, the dry mass of all the sediment in the bottle, and the time a typical grain took to sink through 50 cm of still water (Table 1).

Table 1
SiteTypical grain diameterMass of one grain (g)Sediment in bottle (g)Time to sink 50 cm (s)
Site 12 mm1 × 10⁻²2.53
Site 20.5 mm2 × 10⁻⁴4.09
Site 3150 µm5 × 10⁻⁶1.540
Site 40.04 cm9 × 10⁻⁵3.012
For Sites 1 to 4: typical grain diameter 2 mm, 0.5 mm, 150 µm and 0.04 cm; mass of one grain 1 × 10⁻², 2 × 10⁻⁴, 5 × 10⁻⁶ and 9 × 10⁻⁵ g; sediment in the 500 mL bottle 2.5, 4.0, 1.5 and 3.0 g; time to sink 50 cm 3, 9, 40 and 12 s. Larger grains are heavier and sink faster.

Based on Table 1, which list orders the sites from the largest typical grain diameter to the smallest?

  1. Site 1, Site 2, Site 4, Site 3Answer
  2. Site 3, Site 1, Site 2, Site 4
  3. Site 4, Site 1, Site 2, Site 3
  4. Site 1, Site 3, Site 2, Site 4

How to solve it

  1. From the passage: the four diameters are 2 mm, 0.5 mm, 150 µm and 0.04 cm, three different units.
  2. From background: 0.04 cm × 10 = 0.4 mm and 150 µm ÷ 1,000 = 0.15 mm.
  3. Order 2, 0.5, 0.4, 0.15 mm: Sites 1, 2, 4, 3. Cross-check with the sinking times, 3, 9, 12 and 40 s.

Why each choice is right or wrong

  • A. Correct. In millimeters the diameters are 2 (Site 1), 0.5 (Site 2), 0.4 (Site 4) and 0.15 (Site 3). The sinking times in Table 1, 3, 9, 12 and 40 s, fall in the same order, which agrees.
  • B. Incorrect. This orders the bare numbers 150, 2, 0.5 and 0.04 without converting. 150 µm is only 0.15 mm, the smallest grain.
  • C. Incorrect. This treats 0.04 cm as 4 mm, multiplying by 100 instead of 10. Site 4’s grains are 0.4 mm.
  • D. Incorrect. This treats 150 µm as 1.5 mm, as if 100 µm made 1 mm. From background, 1,000 µm = 1 mm, so 150 µm = 0.15 mm.

Trap Comparing digits instead of amounts

Site 3’s diameter is written 150 and Site 1’s is written 2, yet Site 1’s grains are the biggest. Before you order or compare values, rewrite every value in one unit. The same goes for scientific notation: read the exponent before the leading number, so 5 × 10⁻⁶ is smaller than 9 × 10⁻⁵.