Answer :
Sure! Let's look at how to express the number 0.000000000386 in scientific notation.
Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. A number is written in the form:
[tex]\[ a \times 10^n \][/tex]
where [tex]\( a \)[/tex] is a number greater than or equal to 1 and less than 10, and [tex]\( n \)[/tex] is an integer.
Now, let's convert 0.000000000386 into this form:
1. Identify the Significant Figures: The number is 0.000000000386. We need to move the decimal point to the right so that we have a number between 1 and 10. In this case, 3.86 is the number we want.
2. Count the Decimal Places Moved: To turn 0.000000000386 into 3.86, we move the decimal point 10 places to the right.
3. Write in Scientific Notation: Since we moved the decimal 10 places to the right, the exponent [tex]\( n \)[/tex] will be -10 (negative because we moved the decimal to the right).
Thus, 0.000000000386 can be expressed in scientific notation as:
[tex]\[ 3.86 \times 10^{-10} \][/tex]
Now, let's compare this result with the options given:
- A. [tex]\( 3.86 \times 10^{-10} \)[/tex]
- B. [tex]\( 3.86 \times 10^{10} \)[/tex]
- C. [tex]\( 38.6 \times 10^{-10} \)[/tex]
- D. [tex]\( 123.86 \times 10^{11} \)[/tex]
The correct answer is option A: [tex]\( 3.86 \times 10^{-10} \)[/tex].
Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. A number is written in the form:
[tex]\[ a \times 10^n \][/tex]
where [tex]\( a \)[/tex] is a number greater than or equal to 1 and less than 10, and [tex]\( n \)[/tex] is an integer.
Now, let's convert 0.000000000386 into this form:
1. Identify the Significant Figures: The number is 0.000000000386. We need to move the decimal point to the right so that we have a number between 1 and 10. In this case, 3.86 is the number we want.
2. Count the Decimal Places Moved: To turn 0.000000000386 into 3.86, we move the decimal point 10 places to the right.
3. Write in Scientific Notation: Since we moved the decimal 10 places to the right, the exponent [tex]\( n \)[/tex] will be -10 (negative because we moved the decimal to the right).
Thus, 0.000000000386 can be expressed in scientific notation as:
[tex]\[ 3.86 \times 10^{-10} \][/tex]
Now, let's compare this result with the options given:
- A. [tex]\( 3.86 \times 10^{-10} \)[/tex]
- B. [tex]\( 3.86 \times 10^{10} \)[/tex]
- C. [tex]\( 38.6 \times 10^{-10} \)[/tex]
- D. [tex]\( 123.86 \times 10^{11} \)[/tex]
The correct answer is option A: [tex]\( 3.86 \times 10^{-10} \)[/tex].
