Answer :
To express the number 0.159 in engineering notation, we need to represent it as a number between 1 and 1000 multiplied by a power of ten, where the exponent is a multiple of three.
Let's explore the options provided:
a. [tex]\( 159 \times 10^{-3} \)[/tex]
b. [tex]\( 15.9 \times 10^{-2} \)[/tex]
c. [tex]\( 159 \times 10^3 \)[/tex]
d. [tex]\( 1.59 \times 10 \)[/tex]
Now, we'll check which of these expressions is equal to 0.159:
1. For option a, [tex]\( 159 \times 10^{-3} \)[/tex] means you are moving the decimal point three places to the left:
[tex]\[
159 \times 0.001 = 0.159
\][/tex]
This matches our original number.
2. For option b, [tex]\( 15.9 \times 10^{-2} \)[/tex] means moving the decimal point two places to the left:
[tex]\[
15.9 \times 0.01 = 0.159
\][/tex]
This also matches the original number.
3. For option c, [tex]\( 159 \times 10^3 \)[/tex] means moving the decimal point three places to the right:
[tex]\[
159 \times 1000 = 159000
\][/tex]
This is much larger than 0.159.
4. For option d, [tex]\( 1.59 \times 10 \)[/tex] means moving the decimal point one place to the right:
[tex]\[
1.59 \times 10 = 15.9
\][/tex]
This is also larger than 0.159.
Thus, both options a. [tex]\( 159 \times 10^{-3} \)[/tex] and b. [tex]\( 15.9 \times 10^{-2} \)[/tex] represent 0.159 correctly in engineering notation. However, in standard engineering notation, exponents should ideally be multiples of three, which aligns with option a. [tex]\( 159 \times 10^{-3} \)[/tex].
So, the correct representation in engineering notation is:
a. [tex]\( 159 \times 10^{-3} \)[/tex]
Let's explore the options provided:
a. [tex]\( 159 \times 10^{-3} \)[/tex]
b. [tex]\( 15.9 \times 10^{-2} \)[/tex]
c. [tex]\( 159 \times 10^3 \)[/tex]
d. [tex]\( 1.59 \times 10 \)[/tex]
Now, we'll check which of these expressions is equal to 0.159:
1. For option a, [tex]\( 159 \times 10^{-3} \)[/tex] means you are moving the decimal point three places to the left:
[tex]\[
159 \times 0.001 = 0.159
\][/tex]
This matches our original number.
2. For option b, [tex]\( 15.9 \times 10^{-2} \)[/tex] means moving the decimal point two places to the left:
[tex]\[
15.9 \times 0.01 = 0.159
\][/tex]
This also matches the original number.
3. For option c, [tex]\( 159 \times 10^3 \)[/tex] means moving the decimal point three places to the right:
[tex]\[
159 \times 1000 = 159000
\][/tex]
This is much larger than 0.159.
4. For option d, [tex]\( 1.59 \times 10 \)[/tex] means moving the decimal point one place to the right:
[tex]\[
1.59 \times 10 = 15.9
\][/tex]
This is also larger than 0.159.
Thus, both options a. [tex]\( 159 \times 10^{-3} \)[/tex] and b. [tex]\( 15.9 \times 10^{-2} \)[/tex] represent 0.159 correctly in engineering notation. However, in standard engineering notation, exponents should ideally be multiples of three, which aligns with option a. [tex]\( 159 \times 10^{-3} \)[/tex].
So, the correct representation in engineering notation is:
a. [tex]\( 159 \times 10^{-3} \)[/tex]
