Question

subtract and express the answer in scientific notation.
1 ((8.64 \times 10^{5}) - (6.2 \times 10^{4}))
2 ((3.64 \times 10^{7}) - (9.8 \times 10^{4}))
3 ((6.7 \times 10^{-3}) - (1.2 \times 10^{-4}))
4 ((4.83 \times 10^{-6}) - (4.07 \times 10^{-6}))

Explanation:

Problem 1: $(8.64 \times 10^{5}) - (6.2 \times 10^{4})$

Step 1: Make exponents equal

Convert $8.64 \times 10^{5}$ to $86.4 \times 10^{4}$ (since $10^{5}=10\times10^{4}$).

Step 2: Subtract the coefficients

Subtract $6.2$ from $86.4$: $86.4 - 6.2 = 80.2$.

Step 3: Write in scientific notation

$80.2 \times 10^{4}$ is not in scientific notation. Convert to $8.02 \times 10^{5}$ (because $80.2 = 8.02\times10^{1}$, so $8.02\times10^{1}\times10^{4}=8.02\times10^{5}$).

Step 1: Make exponents equal

Convert $3.64 \times 10^{7}$ to $3640 \times 10^{4}$ (since $10^{7}=1000\times10^{4}$) or convert $9.8 \times 10^{4}$ to $0.0098 \times 10^{7}$. We'll use the second method: $9.8 \times 10^{4}=0.0098 \times 10^{7}$.

Step 2: Subtract the coefficients

$3.64 - 0.0098 = 3.6302$.

Step 3: Write in scientific notation

$3.6302 \times 10^{7}$.

Step 1: Make exponents equal

Convert $6.7 \times 10^{-3}$ to $67 \times 10^{-4}$ (since $10^{-3}=10\times10^{-4}$).

Step 2: Subtract the coefficients

$67 - 1.2 = 65.8$.

Step 3: Write in scientific notation

$65.8 \times 10^{-4}$ is not in scientific notation. Convert to $6.58 \times 10^{-3}$ (because $65.8 = 6.58\times10^{1}$, so $6.58\times10^{1}\times10^{-4}=6.58\times10^{-3}$).

Answer:

$8.02 \times 10^{5}$

Problem 2: $(3.64 \times 10^{7}) - (9.8 \times 10^{4})$