Standard Form
1. We start with the problem:
a) Calculate $ (1.8 \times 10^9) + (6.2 \times 10^7) $ in standard form.
2. Convert the terms so powers of 10 match for easier addition:
$1.8 \times 10^9 = 1.8 \times 10^9$
$6.2 \times 10^7 = 0.062 \times 10^9$
3. Add the coefficients:
$1.8 + 0.062 = 1.862$
4. Combine with the common power of 10:
$1.862 \times 10^9$
5. Answer for part a): $1.862 \times 10^9$
6. Now, for part b) calculate $ (6.4 \times 10^{-11}) - (5.3 \times 10^{-12}) $ in standard form.
7. Express second term with the same power of 10:
$5.3 \times 10^{-12} = 0.53 \times 10^{-11}$
8. Subtract the coefficients:
$6.4 - 0.53 = 5.87$
9. Result in standard form:
$5.87 \times 10^{-11}$
10. Answer for part b): $5.87 \times 10^{-11}$