Question

add and express the answer in scientific notation.
1 ((8.18 \times 10^{1}) + (6.7 \times 10^{-1}))
2 ((4.2 \times 10^{4}) + (7.3 \times 10^{3}))
3 ((9.5 \times 10^{3}) + (4.4 \times 10^{4}))
4 ((9.85 \times 10^{-12}) + (8.3 \times 10^{-13}))

Explanation:

Problem 1: \((8.18 \times 10^{1}) + (6.7 \times 10^{-1})\)

Step 1: Convert to standard form

First, convert each term to standard (decimal) form.
For \(8.18 \times 10^{1}\): \(8.18 \times 10 = 81.8\)
For \(6.7 \times 10^{-1}\): \(6.7 \times \frac{1}{10} = 0.67\)

Step 2: Add the decimal numbers

Add the two decimal numbers: \(81.8 + 0.67 = 82.47\)

Step 3: Express in scientific notation

Now, express \(82.47\) in scientific notation.
We need to write it as \(a \times 10^{n}\) where \(1 \leq a < 10\) and \(n\) is an integer.
\(82.47 = 8.247 \times 10^{1}\)

Problem 2: \((4.2 \times 10^{4}) + (7.3 \times 10^{3})\)

Step 1: Make exponents the same

To add numbers in scientific notation, the exponents must be the same. Let’s convert \(7.3 \times 10^{3}\) to have an exponent of \(4\).
\(7.3 \times 10^{3} = 0.73 \times 10^{4}\) (since \(10^{3} = 10^{4 - 1} = \frac{10^{4}}{10}\), so \(7.3 \times 10^{3} = \frac{7.3}{10} \times 10^{4} = 0.73 \times 10^{4}\))

Step 2: Add the coefficients

Now add the coefficients: \(4.2 + 0.73 = 4.93\)

Step 3: Combine with the common exponent

Combine the sum of the coefficients with \(10^{4}\): \(4.93 \times 10^{4}\)

Problem 3: \((9.5 \times 10^{3}) + (4.4 \times 10^{4})\)

Step 1: Make exponents the same

Convert \(9.5 \times 10^{3}\) to have an exponent of \(4\).
\(9.5 \times 10^{3} = 0.95 \times 10^{4}\) (since \(10^{3} = \frac{10^{4}}{10}\), so \(9.5 \times 10^{3} = \frac{9.5}{10} \times 10^{4} = 0.95 \times 10^{4}\))

Step 2: Add the coefficients

Add the coefficients: \(0.95 + 4.4 = 5.35\)

Step 3: Combine with the common exponent

Combine with \(10^{4}\): \(5.35 \times 10^{4}\)

Problem 4: \((9.85 \times 10^{-12}) + (8.3 \times 10^{-13})\)

Answer:

s:

1. \(8.247 \times 10^{1}\)
2. \(4.93 \times 10^{4}\)
3. \(5.35 \times 10^{4}\)
4. \(1.068 \times 10^{-11}\)