To solve the expression [tex]\( 3 \times 10^{-2} \)[/tex]:
1. Understand the components of the expression:
- The number [tex]\( 3 \)[/tex].
- The term [tex]\( 10^{-2} \)[/tex].
2. Rewrite the term with the negative exponent:
- [tex]\( 10^{-2} \)[/tex] means [tex]\( \frac{1}{10^2} \)[/tex].
3. Calculate the value of the exponent:
- [tex]\( 10^2 = 10 \times 10 = 100 \)[/tex].
4. Replace the term [tex]\( 10^{-2} \)[/tex] with its equivalent fraction:
- [tex]\( 10^{-2} = \frac{1}{100} \)[/tex].
5. Now, multiply the number [tex]\( 3 \)[/tex] by the fraction [tex]\( \frac{1}{100} \)[/tex]:
- [tex]\( 3 \times \frac{1}{100} = \frac{3}{100} \)[/tex].
6. Simplify the fraction:
- [tex]\( \frac{3}{100} = 0.03 \)[/tex].
Thus, [tex]\( 3 \times 10^{-2} = 0.03 \)[/tex].
