Name: Expressing Large Numbers in Standard Form
Uploaded: 2019-07-19
Duration: 7 min 22 s
Description: Any number can be expressed as decimal numbers between 1 and 10 multiplied by a power of 10. In this video, we will learn about expressing large numbers in standard form.

Question

Express the following as product of powers of prime factors.

$3, 200$

Accepted Answer

We know,

We use exponents as a shortcut to represent repeated multiplication. When a number is multiplied with itself $2$ or more times, then we represent it in exponent form.

It can be generalised as $a \times a \times a \times . . . \times n times = a^{n}$ , where $a$ is any non-zero number and $n$ is a natural number and it is read as " $a$ to the power $n$ or $a$ raised to the power $n$ ".

Here $' a'$ is called the base and $' n'$ is called the exponent or index.

Given,

$3200$

Prime factorising, we get:

$\begin{matrix} 2 & 3 & 2 & 0 & 0 \\ 2 & 1 & 6 & 0 & 0 \\ 2 & 8 & 0 & 0 \\ 2 & 4 & 0 & 0 \\ 2 & 2 & 0 & 0 \\ 2 & 1 & 0 & 0 \\ 2 & 5 & 0 \\ 5 & 2 & 5 \\ 5 \end{matrix}$

Writing the number $3200$ as power of prime factors, we have:

$\Rightarrow 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5$

$\Rightarrow 2^{7} \times 5^{2}$

Hence, the required answer is $2^{7} \times 5^{2}$ .

Express the following as product of powers of prime factors.

$3, 200$

Important Questions on Exponents and Powers

Learn and Prepare for any exam you want !

Express the following as product of powers of prime factors. 3,200

Important Questions on Exponents and Powers

Learn and Prepare for any exam you want !

Express the following as product of powers of prime factors.

$3, 200$