Math Monks worksheet on scientific notation word problems.

Let's solve each of these scientific notation word problems step by step and explain the reasoning.

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Problem 1:

The Statue of Liberty is $1.5108 \times 10^2$ feet tall from the top of the pedestal. The pedestal is $1.54 \times 10^2$ feet tall from the foundation. Together, how tall is the Statue of Liberty from the foundation?

#### Step 1: Understand what’s being asked.
We need to add the height of the statue and the pedestal.

- Statue height: $1.5108 \times 10^2 = 151.08$ feet
- Pedestal height: $1.54 \times 10^2 = 154$ feet

#### Step 2: Add them:
$$
151.08 + 154 = 305.08 \text{ feet}
$$

#### Step 3: Convert to scientific notation:
$$
305.08 = 3.0508 \times 10^2
$$

✔ Answer: $ \boxed{3.0508 \times 10^2} $ feet

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Problem 2:

The mass of the moon is about $7.3 \times 10^{22}$ kg. The mass of Earth is $5.9 \times 10^{24}$ kg. The mass of Pluto is $1.3 \times 10^{22}$ kg. Find the combined mass of the moon, Earth, and Pluto. Write your answer in scientific notation.

#### Step 1: Write all values with the same exponent to add them easily.

We’ll convert everything to $10^{24}$:

- Moon: $7.3 \times 10^{22} = 0.073 \times 10^{24}$
- Earth: $5.9 \times 10^{24}$ (already good)
- Pluto: $1.3 \times 10^{22} = 0.013 \times 10^{24}$

#### Step 2: Add:
$$
0.073 + 5.9 + 0.013 = 5.986 \times 10^{24} \text{ kg}
$$

✔ Answer: $ \boxed{5.986 \times 10^{24}} $ kg

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Problem 3:

In the United States, people use approximately 2,240,000,000 pounds of bread in a year. How can we write this number in scientific notation?

#### Step 1: Move the decimal point so there’s only one non-zero digit to the left.

$$
2,240,000,000 = 2.24 \times 10^9
$$

(Count the zeros: 9 digits after 2.24)

✔ Answer: $ \boxed{2.24 \times 10^9} $

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Problem 4:

The diameter of Mars is $6.8 \times 10^3$ kilometers. The diameter of Earth is about $1.2763 \times 10^4$ km. Find how much greater is Earth's diameter than the diameter of Mars?

#### Step 1: Make sure both numbers have the same exponent.

Convert $6.8 \times 10^3$ to $10^4$:

$$
6.8 \times 10^3 = 0.68 \times 10^4
$$

#### Step 2: Subtract:
$$
1.2763 \times 10^4 - 0.68 \times 10^4 = (1.2763 - 0.68) \times 10^4 = 0.5963 \times 10^4
$$

#### Step 3: Convert to proper scientific notation:
$$
0.5963 \times 10^4 = 5.963 \times 10^3
$$

✔ Answer: $ \boxed{5.963 \times 10^3} $ km

Earth's diameter is 5,963 km greater than Mars'.

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Problem 5:

An airplane traveled at a speed of $5.7 \times 10^2$ miles per hour for $1.4 \times 10^1$ hours. How far did the plane travel?

Use the formula:
$$
\text{Distance} = \text{Speed} \times \text{Time}
$$

#### Step 1: Multiply the numbers:
$$
(5.7 \times 10^2) \times (1.4 \times 10^1) = (5.7 \times 1.4) \times 10^{2+1}
$$

$$
5.7 \times 1.4 = 7.98
$$

$$
10^{2+1} = 10^3
$$

So:
$$
7.98 \times 10^3 \text{ miles}
$$

✔ Answer: $ \boxed{7.98 \times 10^3} $ miles

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✔ Final Answers Summary:

1. $ \boxed{3.0508 \times 10^2} $ feet
2. $ \boxed{5.986 \times 10^{24}} $ kg
3. $ \boxed{2.24 \times 10^9} $ pounds
4. $ \boxed{5.963 \times 10^3} $ km
5. $ \boxed{7.98 \times 10^3} $ miles

Let me know if you'd like these explained further or want a printable version!