Lesson 14
Adding and Subtracting with Scientific Notation
Let’s add and subtract using scientific notation to answer questions about animals and the solar system.
Problem 1
Evaluate each expression, giving the answer in scientific notation:
- \(5.3 \times 10^4 + 4.7 \times 10^4\)
- \(3.7 \times 10^6 - 3.3 \times 10^6\)
- \(4.8 \times 10^{\text-3} + 6.3 \times 10^{\text-3}\)
- \(6.6 \times 10^{\text-5} - 6.1 \times 10^{\text-5}\)
Problem 2
- Write a scenario that describes what is happening in the graph.
- What is happening at 5 minutes?
- What does the slope of the line between 6 and 8 minutes mean?
![Coordinate plane, time in minutes, 0 to 8, distance in kilometers, 0 to 5. Line segments connect the origin to 2 comma 1, 2 point 5 comma 1, 4 point 5 comma 2, 5 point 5 comma 2, 8 comma 4 point 5.](https://cms-im.s3.amazonaws.com/Koa9yeYQerjR4gj4JKPAFaSE?response-content-disposition=inline%3B%20filename%3D%228-8.5.PP.C.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.PP.C.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033745Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e81ab4f6e4ab3e141dd6441edfccf7d0ac01415e7e090bb74d880b370db15532)
Problem 3
Apples cost $1 each. Oranges cost $2 each. You have $10 and want to buy 8 pieces of fruit. One graph shows combinations of apples and oranges that total to $10. The other graph shows combinations of apples and oranges that total to 8 pieces of fruit.
![Coordinate plane, x, number of apple, y, number of oranges.](https://cms-im.s3.amazonaws.com/hUBzFZuf5v81fxSZ4FWA4uie?response-content-disposition=inline%3B%20filename%3D%228-8.4.PP.C.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%278-8.4.PP.C.Image.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033745Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a2855bfd8fa52e23872ab5f5cee4de844265572d1d44bc3eb877cb736872a0e1)
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Name one combination of 8 fruits shown on the graph that whose cost does not total to $10.
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Name one combination of fruits shown on the graph whose cost totals to $10 that are not 8 fruits all together.
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How many apples and oranges would you need to have 8 fruits that cost $10 at the same time?
Problem 4
Solve each equation and check your solution.
\(\text-2(3x-4)=4(x+3)+6\)
\(\frac12(z+4)-6=\text-2z+8\)
\(4w-7=6w+31\)
Problem 5
Ecologists measure the body length and wingspan of 127 butterfly specimens caught in a single field.
- Draw a line that you think is a good fit for the data.
- Write an equation for the line.
- What does the slope of the line tell you about the wingspans and lengths of these butterflies?
![Scatterplot, wingspan in millimeters, body length in millimeters. Please request assistance.](https://cms-im.s3.amazonaws.com/1qwT2Gh5DaqpAMgxcZP33uZi?response-content-disposition=inline%3B%20filename%3D%228-8.6.PP.B.Image.20.png%22%3B%20filename%2A%3DUTF-8%27%278-8.6.PP.B.Image.20.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033745Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=642b79edeeb68d8814e3d675301e94a446266922aab12734d28e178febe26aa9)
Problem 6
The two triangles are similar. Find \(x\).
![Two triangles. The first has acute angles marked 46 degrees and x degrees. The second has an obtuse marked 106 degrees.](https://cms-im.s3.amazonaws.com/idy2ZBdpMfi5f4Pq7iq5T8Y9?response-content-disposition=inline%3B%20filename%3D%228-8.2.B.PP.Image.08.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.B.PP.Image.08.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033745Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=20bd4836f603f92ea604c91fa565f68e88b98b60926b24152b0b31acacf73b37)