Scientific Notation- Word Problems worksheet - Free Printable

Let’s solve each problem one by one, step by step.

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Problem 1:

Mrs. Rolle’s class is studying the solar system. The circumference of the Earth is about 24,900 miles. Express this number in scientific notation.

Scientific notation means writing a number as:
a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

Start with 24,900.

Move the decimal point so that only one non-zero digit is to the left of the decimal.

24,900 → move decimal 4 places to the left → becomes 2.49

So, 24,900 = 2.49 × 10⁴

✔ Final Answer for #1: 2.49 × 10⁴

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Problem 2:

The speed of light is approximately 6.71 × 10⁸ miles per hour. Express this number in standard form.

Standard form means write it out as a regular number (no exponents).

6.71 × 10⁸ means move the decimal point 8 places to the right.

6.71 → add zeros as needed:

6.71 → 67.1 → 671 → 6,710 → 67,100 → 671,000 → 6,710,000 → 67,100,000 → 671,000,000

That’s 8 moves.

✔ Final Answer for #2: 671,000,000

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Problem 3:

Earth is approximately 9.3 × 10⁷ miles from the sun and Saturn is approximately 8.87 × 10⁸ miles from the sun. Approximately, how much further is Saturn from the sun than Earth?

We need to subtract Earth’s distance from Saturn’s distance:

Saturn – Earth = (8.87 × 10⁸) – (9.3 × 10⁷)

But the powers of 10 are different. Let’s make them the same.

Convert 9.3 × 10⁷ to something × 10⁸:

9.3 × 10⁷ = 0.93 × 10⁸

Now subtract:

8.87 × 10⁸ – 0.93 × 10⁸ = (8.87 – 0.93) × 10⁸ = 7.94 × 10⁸

✔ Final Answer for #3: 7.94 × 10⁸

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Problem 4:

A factory can make 3 × 10⁴ t-shirts in a day. How many t-shirts can the factory make in 2.5 × 10² days?

Multiply the two numbers:

(3 × 10⁴) × (2.5 × 10²)

First, multiply the coefficients: 3 × 2.5 = 7.5

Then, multiply the powers of 10: 10⁴ × 10² = 10^(4+2) = 10⁶

So total = 7.5 × 10⁶

✔ Final Answer for #4: 7.5 × 10⁶

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Problem 5:

John normally drives 3 × 10¹ miles every day. Today, however, he has to drive Knoxville, Tennessee which is 3 × 10² miles away. How many times greater did John have to drive today than on a normal day?

This is asking: “Today’s distance ÷ Normal distance”

So: (3 × 10²) ÷ (3 × 10¹)

Divide coefficients: 3 ÷ 3 = 1

Divide powers of 10: 10² ÷ 10¹ = 10^(2–1) = 10¹

So result = 1 × 10¹ = 10

✔ Final Answer for #5: 10

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Final Answer:
1. 2.49 × 10⁴
2. 671,000,000
3. 7.94 × 10⁸
4. 7.5 × 10⁶
5. 10