Given data

Concept: Unit Conversion – SI prefix recognition

SI prefixes represent standard powers of ten used to scale units. Each prefix has a fixed meaning:

• micro ($\mu$) means one millionth: $10^{-6}$
• deca (da) means ten: $10^{1} = 10$
• mega (M) means one million: $10^{6}$
• giga (G) means one billion: $10^{9}$
• femto (f) means one quadrillionth: $10^{-15}$

Matching prefixes to their correct multiples from the given list:

| Prefix | Correct Multiple |

|--------|------------------| …

The metric system uses prefixes to express very large or very small quantities without writing strings of zeros. Each prefix corresponds to a specific power of ten, and these are standardized internationally. The pattern is logical: prefixes for large numbers (kilo, mega, giga) use positive exponents, while prefixes for small numbers (milli, micro, nano) use negative exponents.

The key is to remember a few anchor points and the progression. For large numbers, the sequence goes: kilo ($10^3$), mega ($10^6$), giga ($10^9$), tera ($10^{12}$) — each step multiplies by $1000$ or adds $3$ to the exponent. For small numbers: milli ($10^{-3}$), micro ($10^{-6}$), nano ($10^{-9}$), pico ($10^{-12}$), femto ($10^{-15}$) — each step divides by $1000$ or subtracts $3$ from the exponent.

Let me match each prefix with its correct multiple:

1. micro (μ): The prefix "micro" means one-millionth. A micrometer is one-millionth of a meter, a microsecond is one-millionth of a second. This corresponds to $10^{-6}$.

2. deca (da): The prefix "deca" means ten. A decameter is ten meters, a decaliter is ten liters. This is simply $10^1 = 10$.

3. mega (M): The prefix "mega" means one million. A megabyte is roughly a million bytes, a megawatt is a million watts. This corresponds to $10^6$.

4. giga (G): The prefix "giga" means one billion (in the short-scale system used in science). A gigabyte is a billion bytes, a gigahertz is a billion hertz. This corresponds to $10^9$. …

Method: Standard Prefix Table Matching

This is a direct recall and match method — you match each prefix to its correct power-of-10 multiple using the standard SI prefix table.

Steps

1. Recall the standard SI prefix values (from memory or a reference table):

   Prefix	Symbol	Multiple
   micro	$\mu$	$10^{-6}$
   deca	da	$10^{1}$
   mega	M	$10^{6}$
   giga	G	$10^{9}$
   femto	f	$10^{-15}$

2. Match each given prefix to its correct multiple:

   • (i) micro → $10^{-6}$
   • (ii) deca → $10$ (which is $10^{1}$)
   • (iii) mega → $10^{6}$
   • (iv) giga → $10^{9}$
   • (v) femto → $10^{-15}$

3. Write the correct matches:

   • (i) micro → $10^{-6}$
   • (ii) deca → $10$
   • (iii) mega → $10^{6}$
   • (iv) giga → $10^{9}$
   • (v) femto → $10^{-15}$

--- …

Here are the common mistakes students make when matching prefixes to their multiples, along with how to avoid each.

1. Confusing micro ($\mu$) with mega (M)

The Mistake:

Students often swap micro ($10^{-6}$) and mega ($10^{6}$) because both sound similar or because they misremember the sign of the exponent.

How to Avoid:

• Remember the mnemonic:
  • micro = millionth = $10^{-6}$ (small)
  • mega = million = $10^{6}$ (large)
• Visualise the size: micro is for tiny things (e.g., micrometres), mega is for huge things (e.g., megawatts).

2. Forgetting that deca means 10, not 100

The Mistake:

Some students match deca with $10^{2}$ (hecto) or $10^{3}$ (kilo) because they think "deca" sounds like "deci" or "deka" is unfamiliar.

How to Avoid:

• Learn the prefix ladder:
  • deci = $10^{-1}$
  • deca = $10^{1}$ (10)
  • hecto = $10^{2}$
  • kilo = $10^{3}$
• Practise writing them in order from smallest to largest.

3. Mixing up giga and femto

The Mistake:

Giga ($10^{9}$) and femto ($10^{-15}$) are often swapped because both are less common in daily life.

How to Avoid:

• Use a memory trick:
  • Giga = Giant = $10^{9}$ (big)
  • Femto = Feeble = $10^{-15}$ (tiny)
• Write the full table from memory once a day until it sticks.

4. Ignoring the negative exponent for small prefixes

The Mistake:

Students match micro and femto with positive exponents (e.g., micro = $10^{6}$) because they forget that small prefixes have negative powers.

How to Avoid:

• Rule of thumb:
  • Prefixes for large quantities: mega, giga, tera → positive exponents
  • Prefixes for small quantities: micro, nano, femto → negative exponents
• Always check: if the prefix describes something small, the exponent must be negative.

5. Not memorising the standard prefix table

The Mistake: …