Printable math worksheet featuring six scientific notation word problems for students to solve.

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

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Problem 1:

Alpha Centauri is 4.3 light years away.
1 light year = 5,865,696,000,000 miles.

We need to multiply:
4.3 × 5,865,696,000,000

First, write both numbers in scientific notation:

4.3 = 4.3 × 10⁰
5,865,696,000,000 = 5.865696 × 10¹²

Now multiply:

(4.3 × 5.865696) × 10¹²
= 25.2224928 × 10¹²

Convert to proper scientific notation (one digit before decimal):

25.2224928 × 10¹² = 2.52224928 × 10¹³

Rounded reasonably? The original numbers have 2 and 7 significant digits — 4.3 has 2, so we should round to 2 significant digits.

→ 2.5 × 10¹³ miles

✔ Final Answer for #1: 2.5 × 10¹³ miles

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Problem 2:

Americans eat 1,200,000,000 pounds of hamburger per year.
Each hamburger is a quarter-pounder → 0.25 pounds per burger.

Number of hamburgers = total weight ÷ weight per burger
= 1,200,000,000 ÷ 0.25

Dividing by 0.25 is same as multiplying by 4:

1,200,000,000 × 4 = 4,800,000,000

In scientific notation:
4,800,000,000 = 4.8 × 10⁹

✔ Final Answer for #2: 4.8 × 10⁹ hamburgers

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Problem 3:

Red blood cell width = 4.0 × 10⁻⁵ inches
Total cells = 2.5 × 10¹³

If lined up end to end, total length in inches =
(4.0 × 10⁻⁵) × (2.5 × 10¹³)
= (4.0 × 2.5) × 10⁻⁵⁺¹³
= 10.0 × 10⁸
= 1.0 × 10⁹ inches

But question asks for feet.
There are 12 inches in a foot.

So divide by 12:
1.0 × 10⁹ 12 = ?

1.0 × 10⁹ = 1,000,000,000
1,000,000,000 ÷ 12 ≈ 83,333,333.33...

In scientific notation:
≈ 8.333... × 10⁷ feet

Round to 2 significant figures? Original data: 4.0 (2 sig fig), 2.5 (2 sig fig) → answer should have 2 sig fig.

→ 8.3 × 10⁷ feet

✔ Final Answer for #3: 8.3 × 10⁷ feet

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Problem 4:

Earth age = 4.54 billion years = 4,540,000,000 years
Average life span = 70 years

Number of lives = Earth age ÷ life span
= 4,540,000,000 ÷ 70

Calculate:

4,540,000,000 ÷ 70 = 64,857,142.857...

Standard notation: 64,857,143 (rounded to nearest whole number)

Scientific notation:
64,857,143 = 6.4857143 × 10⁷

Round to 3 significant figures? Earth age given as 4.54 (3 sig fig), life span 70 (could be 1 or 2 — assume 2). So let’s use 2 sig fig.

→ 6.5 × 10⁷

But since it says “express in both”, we’ll give exact calculation rounded reasonably.

Actually, 4.54 billion has 3 sig fig, 70 might be exact? Let’s keep 3 sig fig for safety.

64,857,143 → 6.49 × 10⁷ (if rounding to 3 sig fig)

Wait — 4.54 / 70 = 0.064857... × 10⁹ = 6.4857 × 10⁷ → yes.

Best to present:

Standard: 64,857,143
Scientific: 6.49 × 10⁷ (rounded to 3 significant figures)

But maybe they want exact division? Since 4.54 billion is likely approximate, we’ll go with 3 sig fig.

✔ Final Answer for #4:
Standard: 64,857,143
Scientific: 6.49 × 10⁷

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Problem 5:

Men: 10,000 words/day
Women: 25,000 words/day
Earth population: 6 billion = 6,000,000,000
Half men, half women → 3 billion men, 3 billion women

Words by men per day:
3,000,000,000 × 10,000 = 30,000,000,000,000 = 3.0 × 10¹³

Words by women per day:
3,000,000,000 × 25,000 = 75,000,000,000,000 = 7.5 × 10¹³

Difference:
7.5 × 10¹³ - 3.0 × 10¹³ = 4.5 × 10¹³

✔ Final Answer for #5: 4.5 × 10¹³ more words spoken by women each day

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Problem 6:

This is open-ended — you create your own problem using a statistic from research.

Example (just for reference — not part of answer):

> The average human heart beats about 100,000 times per day. How many times does it beat in a year? Express in scientific notation.

But since this is for the student to do, we don’t solve it.

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Now, compiling all final answers:

Final Answer:
1. 2.5 × 10¹³ miles
2. 4.8 × 10⁹ hamburgers
3. 8.3 × 10⁷ feet
4. Standard: 64,857,143; Scientific: 6.49 × 10⁷
5. 4.5 × 10¹³ more words
6. [Student creates their own]