To determine the Young's modulus of a wire, the formula is Y = (F/A).(L/Δl); where L= length, A= area of cross- section of the wire, ΔL = Change in length of the wire when stretched with a force F. The conversion factor to change it from CGS to MKS system is

To find the conversion factor for Young's modulus from the CGS system to the MKS system, we first need to determine its dimensions and units in both systems.

Young's modulus is given by the formula:
$Y=\frac{F}{A}·\frac{L}{\Delta l}$

Let's analyze the units of the quantities involved:
- Force ($F$) has dimensions of $\left[ML{T}^{-2}\right]$.
- Area of cross-section ($A$) has dimensions of $\left[L^2\right]$.
- Length ($L$) and change in length ($\Delta l$) both have dimensions of length $\left[L\right]$, so the ratio $\frac{L}{��l}$ is dimensionless.

Therefore, the dimensional formula of Young's modulus ($Y$) is:
$\left[Y\right]=\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]}=\left[M{L}^{-1}{T}^{-2}\right]$

Now, let's write the units of Young's modulus in both systems:
- In the CGS system, the unit is $\text{g}·{\text{cm}}^{-1}·{\text{s}}^{-2}$ (or dyne/cm²).
- In the MKS system, the unit is $\text{kg}·{\text{m}}^{-1}·{\text{s}}^{-2}$ (or $\text{N/m}{2}^{}$).

Let's convert 1 CGS unit of Young's modulus to the MKS unit:
$1\text{CGS unit}=1\text{g}·{\text{cm}}^{-1}·{\text{s}}^{-2}$

Substitute the conversion values for mass and length:
- $1\text{g}={10}^{-3}\text{kg}$
- $1\text{cm}={10}^{-2}\text{m}$

This gives:
$1\text{CGS unit}=\left({10}^{-3}\text{kg}\right)·{\left({10}^{-2}\text{m}\right)}^{-1}·{\text{s}}^{-2}$

Simplify the exponents:
$1\text{CGS unit}={10}^{-3}·{10}^2\text{kg}·{\text{m}}^{-1}·{\text{s}}^{-2}$

$1\text{CGS unit}={10}^{-1}\text{MKS unit}=0.1\text{MKS unit}$

Thus, the conversion factor to change Young's modulus from the CGS system to the MKS system is 0.1.