Question

How do you use exponents to write 7.5 million in expanded notation?

Answer 1

Hint: To convert a number in the expanded form break the number in its factored form and then write the similar terms in the exponent form.
The exponent form of $7.5$ million in expanded form writes the complete form of 7.5 million as $7500000$ and then factorizes the number. Then, find the exponential form of the given exponents.

Complete step by step solution:
The given number is $7.5$ million.
Since there are $6$ zeros in a million. Write the million as the power of${10^6}$.
Then, the number becomes $7.5 \times {10^6}$.
Then, the number is,
\[ \Rightarrow 7.5 \times {10^6} = 7500000\]
Consider the factors of $75$ are $3 \times 5 \times 5$ .
Write $5 \times 5$ in the exponent form as ${5^2}$, as the number $5$ is multiplied 2 times.
Then, $75$ in the exponent form is $3 \times {5^2}$.
Then, the number in the exponent form is \[7500000 = 75 \times {10^5}\].
Then, the number is,
\[ \Rightarrow 7500000 = 3 \times {5^2} \times {10^5}\]

The number $7.5$ million in the exponent form is \[3 \times {5^2} \times {10^5}\].

Note:
The exponent is the number of times a number can be multiplied by itself. For example consider a variable $a$ as $a \times a = {a^2}$, then ${a^n}$ represents $a$ multiplied by itself n number of times. The exponent form${a^n}$ is pronounced as a raise to the power n. Where,
${a^0} = 1$ and${a^1} = a$. The other properties are${\left( {ab} \right)^n} = {a^n}{b^n}$, also ${a^n}{a^m} = {a^{m + n}}$.