Scientific Notation/Significant Digits Worksheet 1 - Free Printable

Let's go through each section of the worksheet and verify the answers, then explain the solutions step-by-step.

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Problem 1: Convert each of the following into scientific notation.

Scientific Notation Format:
A number is written in scientific notation as:
$$
a \times 10^n
$$
where $1 \leq |a| < 10$ and $n$ is an integer.

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#### a) 3427
- Move decimal to get one digit before it: $3.427$
- Count how many places moved: 3 places right → exponent = +3
✔ $3.427 \times 10^3$

#### b) 2205.2
- $2.2052 \times 10^3$ (moved 3 places)

#### c) 0.00456
- Move decimal right: $4.56$, moved 3 places → exponent = -3
✔ $4.56 \times 10^{-3}$

#### d) 123.453
- $1.23453 \times 10^2$ (move decimal 2 places left)

#### e) 172
- $1.72 \times 10^2$

#### f) 0.000984
- $9.84 \times 10^{-4}$ (move 4 places right)

#### g) 0.502
- $5.02 \times 10^{-1}$

#### h) 3100.0 × 10²
- First write 3100.0 = $3.1000 \times 10^3$, then multiply by $10^2$:
→ $3.1000 \times 10^{3+2} = 3.1000 \times 10^5$
✔ $3.1000 \times 10^5$

#### i) 0.0114 × 10⁴
- 0.0114 = $1.14 \times 10^{-2}$, so:
→ $1.14 \times 10^{-2} \times 10^4 = 1.14 \times 10^{2}$
✔ $1.14 \times 10^2$

#### j) 107.2
- $1.072 \times 10^2$

#### k) 30.0 × 10⁻²
- 30.0 = $3.00 \times 10^1$, so:
→ $3.00 \times 10^1 \times 10^{-2} = 3.00 \times 10^{-1}$
✔ $3.00 \times 10^{-1}$

#### l) 0.0473
- $4.73 \times 10^{-2}$

#### m) 0.982 × 10⁻³
- $9.82 \times 10^{-4}$ (move decimal one place right → exponent decreases by 1)

#### n) 650.502
- $6.50502 \times 10^2$

#### o) 3.03 × 10¹
- Already in scientific notation: $3.03 \times 10^1$

#### p) 20.4 × 10⁵
- 20.4 = $2.04 \times 10^1$, so:
→ $2.04 \times 10^1 \times 10^5 = 2.04 \times 10^6$
✔ $2.04 \times 10^6$

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✔ All your answers for Problem 1 are correct!

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Problem 2: Determine the number of significant figures

Rules for Significant Figures:
1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros (before first non-zero) are not significant.
4. Trailing zeros are significant only if there’s a decimal point.
5. In scientific notation, all digits in the coefficient are significant.

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#### a) 3427 → 4 sig figs ✔
All non-zero → 4

#### b) 0.00456 → 3 sig figs ✔
Leading zeros not counted → 4,5,6 → 3

#### c) 123.453 → 6 sig figs ✔
All digits significant → 6

#### d) 172 → 3 sig figs ✔
No decimal → trailing zero? No → just 3 digits → 3

#### e) 0.000984 → 3 sig figs ✔
Only 9,8,4 → 3

#### f) 0.502 → 3 sig figs ✔
Leading zero ignored, 5,0,2 → 3 (zero is between non-zeros)

#### g) 3100.0 × 10² → 5 sig figs ✔
3100.0 has 5 sig figs (trailing zero after decimal counts), and ×10² doesn’t change that.

#### h) 0.0114 × 10⁴ → 3 sig figs ✔
0.0114 → 1,1,4 → 3

#### i) 107.2 → 4 sig figs ✔
All digits: 1,0,7,2 → zero is between non-zeros → significant → 4

#### j) 0.0000455 → 3 sig figs ✔
4,5,5 → 3

#### k) 2205.2 → 5 sig figs ✔
All digits → 5

#### l) 0.982 × 10⁻³ → 3 sig figs ✔
Coefficient 0.982 → 9,8,2 → 3

#### m) 0.0473 → 3 sig figs ✔
4,7,3 → 3

#### n) 650.502 → 6 sig figs ✔
All digits → 6

#### o) 3.03 × 10¹ → 3 sig figs ✔
3,0,3 → 3

#### p) 20.4 × 10⁵ → 3 sig figs ✔
20.4 → 2,0,4 → 3

#### q) 20.4 → 3 sig figs ✔
Same as above → 3

✔ All your answers for Problem 2 are correct!

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Problem 3: Convert into standard numeral (decimal) form

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#### a) 1.56 × 10⁴
- Move decimal 4 places right: 15600 ✔

#### b) 0.56 × 10⁻²
- 0.56 → move decimal 2 places left: 0.0056 ✔

#### c) 3.69 × 10⁻²
- Move decimal 2 places left: 0.0369 ✔

#### d) 736.9 × 10⁵
- 736.9 × 100,000 = 73,690,000 ✔
(Or: move decimal 5 places right from 736.9 → 73,690,000)

#### e) 0.00259 × 10⁵
- First: 0.00259 → 2.59 × 10⁻³
- Then: 2.59 × 10⁻³ × 10⁵ = 2.59 × 10² = 259 ✔

#### f) 13.69 × 10⁻²
- Move decimal 2 places left: 0.1369 ✔

#### g) 6.9 × 10⁵
- Move decimal 5 places right: 690,000 ✔

✔ All answers for Problem 3 are correct!

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✔ Final Summary:

All your answers are correct!
You've done a great job with:
- Scientific notation conversion
- Determining significant figures
- Converting back to standard form

Well done, LaShawn! 👏

Let me know if you'd like a summary sheet or explanation of any rule!