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Decide mentally how many nonzero digits each number will have.
Diego, Kiran, and Clare were wondering:
“If Neptune and Saturn were side by side, would they be wider than Jupiter?”
They start by trying to add km and km, the diameters of Neptune and Saturn. Here are the ways they approached the problem. Do you agree with any of them? Explain your reasoning.
Kiran wrote as 49,000 and as 120,000 and added them:
| object | diameter (km) | distance from the Sun (km) |
|---|---|---|
| Sun | ||
| Mercury | ||
| Venus | ||
| Earth | ||
| Mars | ||
| Jupiter |
When you add the distances from the Sun of Mercury, Venus, Earth, and Mars, would you reach as far as Jupiter? Explain or show your reasoning.
Add the diameters of all the objects on the table except the Sun. Which is wider, all of these planets side-by-side, or the sun? Explain or show your reasoning.
The table shows the average mass of one individual creature and an estimated total number of those creatures on Earth. Use the table to answer each question, and explain or show your reasoning.
| creature | total number | mass of one individual (kg) |
|---|---|---|
| humans | ||
| cows | ||
| sheep | ||
| chickens | ||
| ants | ||
| blue whales | ||
| antarctic krill | ||
| zooplankton | ||
| bacteria |
On a farm there was a cow. And on the farm there were 2 sheep. There were also 3 chickens. What is the total mass of the 1 cow, the 2 sheep, the 3 chickens, and the 1 farmer on the farm?
When adding decimal numbers, we need to pay close attention to place value. For example, when we calculate , we need to make sure to add hundredths to hundredths (5 and 0), tenths to tenths (2 and 7), ones to ones (3 and 6), and tens to tens (1 and 0).
We need to take the same care when we add or subtract numbers in scientific notation. For example, suppose we want to find how much farther Earth is from the Sun than Mercury is from the Sun. Earth is about km from the Sun, while Mercury is about km. In order to find we can rewrite this as
Now that both numbers are written in terms of , we can subtract 0.58 from 1.5 to get
Rewriting this in scientific notation, Earth is km farther from the Sun than Mercury is from the Sun.