ChemGem

How to Convert Metric Prefixes (Step-by-Step, with Practice)

A metric prefix is a multiplier on the front of a base unit. Kilo means 1000, so 1 km = 1000 m. Each prefix means the same thing on meters, grams, liters and seconds, so you learn it once.

Spot it, solve it, practice it: 4 steps, 1 worked example, 7 practice problems. Free, no account.

ChemGemUpdated Section 0.1a

The route · 4 steps

  1. Find the prefix row in the table.
  2. Write the link as a factor, with the unit to remove underneath.
  3. Multiply; for powers of ten, add the exponents.
  4. Check by converting back.
Try one now See a worked example
Spot it

How to recognize metric prefix questions

Look for metric prefixes like nano, micro, milli, kilo, or mega (nm, μg, mL, km, MW) that must change to base units or another prefix.

Example wording, with the clue words marked:

A vitamin label lists vitamin B12 in micrograms (μg), but your kitchen scale reads grams. How many micrograms are in 1 g? (1 μg = 10−6 g)

Not sure it’s this type? Compare the neighbors:

Step-by-step

Worked example: metric prefix

The idea

A prefix is a multiplier
1 km = 103 m = 1000 m
1 kg = 103 g = 1000 g
The prefix tells how many base units one prefixed unit is worth. Base units: meter (m), gram (g), liter (L), second (s).
The prefix table
PrefixSymbolPower of tenPlain number1 ___ = ? base unit
megaM1061,000,0001 MW = 1,000,000 W
kilok10310001 km = 1000 m
(base unit)none10011 m = 1 m
decid10−10.11 dL = 0.1 L
centic10−20.011 cm = 0.01 m
millim10−30.0011 mL = 0.001 L
microμ10−60.0000011 μg = 0.000001 g
nanon10−90.0000000011 nm = 0.000000001 m
Each row down is a smaller unit. W is the watt, a unit of power; prefixes work on it the same way.
The exponent counts places
mega (M)10⁶kilo (k)10³base unit10⁰ = 1deci (d)10⁻¹centi (c)10⁻²milli (m)10⁻³micro (μ)10⁻⁶nano (n)10⁻⁹Power of ten
103 = 1000. A negative power is a fraction: 10−3 = 1/1000 = 0.001. More negative means smaller.
How big is that?
PrefixEveryday size
Mega (M)A large power plant: about 1000 MW. A phone photo: often 2 to 5 MB (megabytes), about 2 to 5 million bytes.
Kilo (k)1 km: about a 10 to 12 minute walk. 1 kg: about the mass of 1 L of water.
Base units1 L: a large water bottle. 1 g: about a paper clip or a US dollar bill.
Deci (d)1 dL = 100 mL, a little less than half a cup. Blood sugar tests report mg/dL.
Centi (c)1 cm: about the width of your smallest fingernail.
Milli (m)1 mL: about 20 drops; a teaspoon is about 5 mL. 1 mg: about 15 to 20 grains of table salt (one grain ≈ 0.06 mg).
Micro (μ)A red blood cell: about 7 to 8 μm across. A human hair: roughly 50 to 100 μm thick.
Nano (n)Visible light: about 400 nm (violet) to 700 nm (red). DNA strand: about 2 nm wide. Fingernails grow about 1 nm each second.
One table row, two correct factors (nano)
1 nm = 10−9 m
10−9 m1 nm  or  1 nm10−9 m
Flipped: 1 m = 109 nm
109 nm1 m  or  1 m109 nm
No negative exponent.

Either form works. As in 0.1, put the unit you are removing underneath.

Worked example · 4 steps

A green laser pointer gives light with a wavelength of 532 nm. What is that wavelength in meters? Then convert your answer back to nanometers to check it.

Given532 nm
Findm, then back to nm
Link1 nm = 10−9 m
  1. 1
    Find the link

    Read the nano row of the table.

    1 nm = 10−9 m
  2. 2
    Put nm underneath

    nm is the unit to remove, so it goes on the bottom and cancels.

    532 nm1 × 10−9 m1 nm
  3. 3
    Calculate

    532 = 5.32 × 102, and 2 + (−9) = −7. Three significant figures, like 532.

    532 nm1 × 10−9 m1 nm = 532 × 10−9 m = 5.32 × 10−7 m
  4. 4
    Convert back

    Use the flipped form, 1 m = 109 nm, with m underneath. −7 + 9 = 2.

    5.32 × 10−7 m × 109 nm1 m = 5.32 × 102 nm = 532 nm
  5. ✓
    Answer

    5.32 × 10−7 m, and back to 532 nm.

Your turn

Metric prefix practice problems

Answer first, then check. Hints open one at a time; the answer and full solution open after you try.

Problem 1 of 7 · warm-up

A vitamin label lists vitamin B12 in micrograms (μg), but your kitchen scale reads grams. How many micrograms are in 1 g? (1 μg = 10−6 g)

Hint 1 · the clue

Micro means 10−6, so 1 μg = 10−6 g. Put g underneath.

Hint 2 · the next move

Grams must become micrograms, and the micro prefix link is given: put g underneath so it cancels.

Your path:

  1. Write 1 g
  2. Multiply by 1 μg / 10−6 g
  3. Dividing by 10−6 means multiplying by 106
Answer

Answer: 106 μg (1,000,000 μg)

Full worked solution

What you know: 1 g, and 1 μg = 10−6 g. What you want: micrograms.

  1. Write the input and put g underneath so it cancels: 1 g × (1 μg / 10−6 g).
  2. g cancels, leaving μg. Divide: 1 ÷ 10−6 = 106, because dividing by 10−6 is the same as multiplying by 106.
  3. The answer is 106 μg (1,000,000 μg). This is a definition, so it is exact.

Check: A microgram is far smaller than a gram, so it takes many of them. Reverse it: 106 μg × 10−6 g/μg = 100 g = 1 g.

Watch out: 1000 μg is only 1 mg, not 1 g. Micro is 1000 times smaller than milli.

Your route: Write the link, 1 μg = 10−6 g → Put g underneath → Cancel and calculate.

Answer: 106 μg (1,000,000 μg)

Problem 2 of 7

A large wind turbine is rated at 3.5 MW. The power company’s spreadsheet lists power in watts (W). What number goes in the spreadsheet? (1 MW = 106 W)

Hint 1 · the clue

Capital M is mega, a million. Put MW underneath.

Hint 2 · the next move

Megawatts (MW) must become watts (W): the mega prefix means 106, so convert with MW underneath.

Your path:

  1. Write the power in MW
  2. Multiply by 106 W / 1 MW
  3. MW cancels; write in scientific notation
Answer

Answer: 3.5 × 106 W

Full worked solution

What you know: 3.5 MW, and 1 MW = 106 W. What you want: watts.

  1. Put MW underneath so it cancels: 3.5 MW × (106 W / 1 MW).
  2. MW cancels, leaving W. Multiply: 3.5 × 106 W, which is 3.5 million watts.
  3. 3.5 has two significant figures, and 1 MW = 106 W is exact. The answer is 3.5 × 106 W.

Check: A watt is much smaller than a megawatt, so the number grows. Reverse it: 3.5 × 106 W ÷ 106 W/MW = 3.5 MW.

Watch out: 3.5 mW, with a lowercase m, would be 3.5 milliwatts, a billion times less power.

Your route: Write the input → Put MW underneath → Multiply by 106 → Keep two significant figures.

Answer: 3.5 × 106 W

Problem 3 of 7

A red laser pointer shines light with a wavelength of 650 nm. A physics formula needs the wavelength in meters. What is it in meters? (1 nm = 10−9 m)

Hint 1 · the clue

Put nm underneath, then write 650 × 10−9 in scientific notation.

Hint 2 · the next move

A wavelength in nm is wanted in meters: the nano prefix means 10−9, so convert nm to m.

Your path:

  1. Write the wavelength in nm
  2. Multiply by 10−9 m / 1 nm
  3. Fix coefficient; add exponents
Answer

Answer: 6.5 × 10−7 m

Full worked solution

What you know: 650 nm, and 1 nm = 10−9 m. What you want: meters.

  1. Put nm underneath so it cancels: 650 nm × (10−9 m / 1 nm).
  2. nm cancels, leaving m. Multiply: 650 × 10−9 m.
  3. Fix the coefficient: 650 = 6.5 × 102, so the result is 6.5 × 102 × 10−9 m. Add the exponents: 2 + (−9) = −7.
  4. The trailing zero in 650 has no decimal point after it, so it is ambiguous (see 0.3); here treat it as not significant, giving two significant figures. The answer is 6.5 × 10−7 m.

Check: A meter is far bigger than a nanometer, so the number gets very small: 6.5 × 10−7 m = 0.00000065 m. Reverse it: 6.5 × 10−7 m × 109 nm/m = 6.5 × 102 nm = 650 nm.

Watch out: Moving the decimal point two places left makes the coefficient smaller, so the exponent goes up by 2, from −9 to −7. Writing 6.5 × 10−11 m moves it the wrong way.

Your route: Put nm underneath → Multiply by 10−9 → Fix the coefficient → Round.

Answer: 6.5 × 10−7 m

Problem 4 of 7

A charity fun run is 2.5 km long. The volunteers mark the course in meters. How many meters long is it? (1 km = 1000 m)

Hint 1 · the clue

Kilo means 1000. A meter is smaller than a kilometer, so expect a bigger number.

Hint 2 · the next move

Kilometers are given and meters are asked for: kilo means 1000, so one factor converts km to m.

Your path:

  1. Write the distance in km
  2. Multiply by 1000 m / 1 km
  3. km cancels, leaving m
Answer

Answer: 2500 m

Full worked solution

What you know: 2.5 km, and 1 km = 1000 m. What you want: meters.

  1. Put km underneath so it cancels: 2.5 km × (1000 m / 1 km).
  2. km cancels, leaving m. Multiply: 2.5 × 1000 = 2500. The answer is 2500 m.

Check: A meter is smaller than a kilometer, so you need more of them. Reverse it: 2500 ÷ 1000 = 2.5 km. At 10 to 12 minutes per kilometer, this is about a 25 to 30 minute walk.

Watch out: 2.5 has two significant figures. Writing 2.5 × 103 m shows that more clearly than 2500 m.

Your route: Write the input → Put km underneath → Multiply by 1000.

Answer: 2500 m

Problem 5 of 7

Over one month, an automatic pipette in a research lab dispenses a total of 4.2 × 106 μL of buffer. How many liters of buffer is that? (1 μL = 10−6 L)

Hint 1 · the clue

Put μL underneath. When you multiply powers of ten, add the exponents.

Hint 2 · the next move

Microliters (μL) in scientific notation must become liters: use the micro link and add exponents.

Your path:

  1. Write the volume in μL
  2. Multiply by 10−6 L / 1 μL
  3. μL cancels; add the exponents
Answer

Answer: 4.2 L

Full worked solution

What you know: 4.2 × 106 μL, and 1 μL = 10−6 L. What you want: liters.

  1. Put μL underneath so it cancels: 4.2 × 106 μL × (10−6 L / 1 μL).
  2. μL cancels, leaving L. Add the exponents: 6 + (−6) = 0, so the result is 4.2 × 100 L.
  3. 100 = 1, and 4.2 has two significant figures. The answer is 4.2 L.

Check: A microliter is tiny, so it takes millions of them to fill a few liters. Reverse it: 4.2 L × 106 μL/L = 4.2 × 106 μL.

Watch out: Multiplying by 106 instead gives 4.2 × 1012, which means the factor was upside down and μL would not cancel.

Your route: Write the input → Put μL underneath → Add the exponents.

Answer: 4.2 L

Problem 6 of 7

A wood splinter is about 1 mm wide. A single bacterium is about 1 μm long. Which unit is larger, 1 mm or 1 μm, and how many times larger is it?

Hint 1 · the clue

Write both in meters: milli means 10−3 and micro means 10−6. The less negative exponent is the larger amount.

Hint 2 · the next move

Two prefixes, milli and micro, are compared: write each as a power of ten, then divide larger by smaller.

Your path:

  1. mm = 10−3 m; μm = 10−6 m
  2. Less negative exponent is larger
  3. Divide larger by smaller to compare
Answer

Answer: 1 mm is larger, by 1000 times

Full worked solution

What you know: 1 mm = 10−3 m and 1 μm = 10−6 m, because milli means 10−3 and micro means 10−6. What you want: which is larger, and by how many times.

  1. Compare the exponents: −3 is less negative than −6, so 10−3 m is the larger length.
  2. Divide the larger by the smaller: 10−3 m ÷ 10−6 m = 10−3 − (−6) = 103 = 1000. The meters cancel, so the ratio has no unit.
  3. The answer is 1 mm is larger, by 1000 times.

Check: In plain numbers, 0.001 m ÷ 0.000001 m = 1000. That fits the picture: you can see a splinter, but you need a microscope for a bacterium.

Watch out: 6 looks bigger than 3, but 10−6 is the smaller number. A more negative exponent means a smaller amount.

Your route: Write both in meters → Compare the exponents → Divide.

Answer: 1 mm is larger, by 1000 times

Problem 7 of 7

A vitamin D tablet contains 25 μg of vitamin D. What is that mass in grams? (1 μg = 10−6 g)

Hint 1 · the clue

Micro (μ) means 10−6. Put μg underneath, then write 25 × 10−6 in scientific notation.

Hint 2 · the next move

Micrograms (μg) must become grams: the micro prefix means 10−6, so put μg underneath.

Your path:

  1. Write the mass in μg
  2. Multiply by 10−6 g / 1 μg
  3. Fix coefficient; add exponents
Answer

Answer: 2.5 × 10−5 g

Full worked solution

What you know: 25 μg, and 1 μg = 10−6 g. What you want: grams.

  1. Read the prefix: micro (μ) is 10−6, so each μg is a millionth of a gram.
  2. Put μg underneath so it cancels: 25 μg × (10−6 g / 1 μg) = 25 × 10−6 g.
  3. Fix the coefficient: 25 = 2.5 × 101, and 1 + (−6) = −5. The answer is 2.5 × 10−5 g, two significant figures like 25.

Check: A microgram is far smaller than a gram, so the number in grams must be far smaller than 25. Reverse it: 2.5 × 10−5 g × (106 μg / 1 g) = 2.5 × 101 μg = 25 μg.

Watch out: Multiplying by 106 instead gives 2.5 × 107, a huge number for a tablet, and μg would not cancel. The factor was upside down.

Answer: 2.5 × 10−5 g

Watch out

Common metric prefix mistakes