High School

Which choice correctly expresses the number below in scientific notation?

145,000

A. [tex]$1.45 \cdot 10^6$[/tex]

B. [tex]$1.45 \cdot 10^5$[/tex]

C. [tex]$145 \cdot 10^5$[/tex]

D. [tex]$145 \cdot 10^3$[/tex]

E. [tex]$1.45 \cdot 10^4$[/tex]

F. [tex]$14.5 \cdot 10^4$[/tex]

Answer :

Sure! Let's convert the number 145,000 to scientific notation step-by-step.

Step 1: Identify the Base Number
We need to express 145,000 as a product of a number between 1 and 10 and a power of 10. To do this, we move the decimal point to get a number between 1 and 10.

The number [tex]\(145,000\)[/tex] can be written as [tex]\(1.45\)[/tex] with the decimal point moved 5 places to the left.

Step 2: Determine the Power of 10
Since we moved the decimal point 5 places to the left, we raise 10 to the power of 5.

Step 3: Write the Number in Scientific Notation
Combining these results, 145,000 can be written in scientific notation as:

[tex]\[ 1.45 \times 10^5 \][/tex]

So the correct answer is:

[tex]\[ B. \, 1.45 \times 10^5 \][/tex]

This concludes the conversion of 145,000 to scientific notation.