Scientific Notation Word Problems GC Practice | PDF - Free Printable

Let’s solve each problem one by one.

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Problem 1:

Fair Bluff population: 9.8 × 10⁴
Tabor City population: 2.5 × 10⁴

To find how many times larger Fair Bluff is than Tabor City, divide the two numbers:

(9.8 × 10⁴) ÷ (2.5 × 10⁴) = (9.8 ÷ 2.5) × (10⁴ ÷ 10⁴) = 3.92 × 1 = 3.92

Since the question says “about”, we can round to about 4 times larger.

✔ Check: 2.5 × 4 = 10 → close to 9.8 — makes sense.

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Problem 2:

Virus diameter: 2.0 × 10⁻⁸ mm
Bacteria diameter: 2.0 × 10⁻⁶ mm

We want to compare bacteria size to virus size → divide bacteria by virus:

(2.0 × 10⁻⁶) ÷ (2.0 × 10⁻⁸) = (2.0 ÷ 2.0) × (10⁻⁶ ÷ 10⁻⁸) = 1 × 10² = 100

So the bacteria is 100 times larger than the virus.

Looking at options:
a) about 10 times smaller → no
b) about 10 times larger → no
c) about 100 times smaller → no
d) about 100 times larger → ✔ YES

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Problem 3:

Red panda weight: 5.0 × 10³ grams
Giant panda weight: 1.5 × 10⁵ grams

Divide giant panda by red panda:

(1.5 × 10⁵) ÷ (5.0 × 10³) = (1.5 ÷ 5.0) × (10⁵ ÷ 10³) = 0.3 × 10² = 30

So the giant panda is 30 times larger.

✔ Check: 5.0 × 10³ = 5,000; 1.5 × 10⁵ = 150,000 → 150,000 ÷ 5,000 = 30 — correct.

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Problem 4:

Speed of light: 3.0 × 10⁸ m/s
Speed of sound: 3.0 × 10² m/s

Divide speed of light by speed of sound:

(3.0 × 10⁸) ÷ (3.0 × 10²) = (3.0 ÷ 3.0) × (10⁸ 10²) = 1 × 10⁶ = 1,000,000

So light is 1 million times faster than sound.

✔ Check: 10⁸ 10² = 10⁶ — yes.

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Final Answers:

1. About 4 times larger
2. d) about 100 times larger
3. About 30 times larger
4. About 1,000,000 times faster