Measurement, time & conversions · Topic 12 of 15

Metric Units & Conversions

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Math · metric units

Meter, gram and liter scale by powers of ten; to convert, move the decimal point one place per prefix step.

01 · The prefixkilo- = 1,000 (1 kg = 1,000 g)

02 · Memorize1 g = 1,000 mg · 1 L = 1,000 mL

03 · Moving the decimalSmaller unit: decimal moves right

Base units: meter (length), gram (mass), liter (volume) must know

To a smaller unit move the decimal right; to a larger unit, left must know

kg → g → mg → mcg: each step is × 1,000 (3 places)

kilo- = 1,000 × (1 kg = 1,000 g; 1 km = 1,000 m) must know

milli- = 1/1,000: 1 g = 1,000 mg; 1 L = 1,000 mL must know

centi- = 1/100: 1 m = 100 cm; 1 cm = 10 mm

micro- = 1/1,000,000: 1 mg = 1,000 mcg

hecto- = 100, deka- = 10, deci- = 1/10

1 mL = 1 cubic centimeter (cc, cm³)

Place both units on the ladder k · h · da · base · d · c · m

Count the steps: one step = one decimal place (milli → micro = 3)

Move the decimal that many places; fill gaps with zeros

2.5 L = 2,500 mL (3 places right)

750 mg = 0.75 g (3 places left)

0.25 mg = 250 mcg (3 places right)

Commonly confused

Check the direction: 500 mg = 0.5 g, not 500,000 g

Show 3 more facts

Leading zero for amounts under 1: 0.5 g, never .5 g

No trailing zero: write 5 mg, not 5.0 mg

SI base unit of mass is the kilogram, despite the kilo- prefix

Pearl

Smaller unit, bigger number: stepping down to a smaller unit moves the decimal to the right.

Practice this topic, then test the whole section.

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