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How is the number 15,000 written in scientific notation?

A. [tex]$1.5 \times 10^4$[/tex]

B. [tex]$1.5 \times 10^6$[/tex]

C. [tex][tex]$1.5 \times 10^3$[/tex][/tex]

D. [tex]$1.0 \times 10^3$[/tex]


Sagot :

To express the number 15,000 in scientific notation, we follow these steps:

1. Identify the Significant Figures: We identify the non-zero digits of the number. For 15,000, these are 1 and 5.

2. Place the Decimal Point: We place the decimal point after the first non-zero digit. This gives us 1.5.

3. Count the Places: We count how many places we need to move the decimal point to return to the original number. Starting at 1.5, we need to move the decimal point 4 places to the right to get 15,000. This count becomes the exponent of 10 in the scientific notation.

4. Construct the Scientific Notation: Combine the significand (1.5) and the exponent (4) with the base (10). Thus, 15,000 is written as [tex]\(1.5 \times 10^4\)[/tex].

Given the options:
A. [tex]\(1.5 \times 10^4\)[/tex]
B. [tex]\(1.5 \times 10^6\)[/tex]
C. [tex]\(1.5 \times 10^3\)[/tex]
D. [tex]\(1.0 \times 10^3\)[/tex]

The correct scientific notation for 15,000 is [tex]\(1.5 \times 10^4\)[/tex], so the correct choice is:
A. [tex]\(1.5 \times 10^4\)[/tex]