Question

The width of a US letter is $5\times {10}^{-1}$ mm.
A pack of US letters have a width of 10m.
How many US letters are there in the pack?

• A. 20000

Answer 1

The correct option is A 20000
The width of a US letter = $5\times {10}^{-1}mm$.
A pack of US letters have a width of 10m.

You know, $1m=1000mm=10\times 10\times 10mm={10}^1\times {10}^1\times {10}^{1}mm={10}^{1+1+1}mm[\because a^x\times a^y=a^{x+y}]={10}^3\mathrm{mm}$

Width of the pack of the US letters can be written as:$10m=10\times 1m=10\times {10}^{3}mm={10}^{1+3}mm[\because a^x\times a^y=a^{x+y}]={10}^{4}mm$

∴ Number of US letters in the pack will be
$\frac{{10}^4}{5\times {10}^{-1}}=\frac{{10}^{4-(-1)}}{5}=\frac{{10}^{4+1}}{5}[\because \frac{a^x}{a^y}=a^{x-y}]=\frac{{10}^5}{5}=\frac{{10}^{1+1+1+1+1}}{5}=\frac{10\times 10\times 10\times 10\times 10}{5}=2\times 10\times 10\times 10\times 10=20,000$

So, the number of US letters in the pack will be = 20000.