Significant Figure and Scientific Notation Worksheet with Answers ... - Free Printable

Let's solve each part of the Significant Figures and Scientific Notation Worksheet step by step.

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1. Convert each of the following into scientific notation

Scientific notation is written 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 decimal:
3.427 × 10³

b) 0.00456
Move decimal 3 places right:
4.56 × 10⁻³

c) 123,453
→ 1.23453 × 10⁵

d) 172
→ 1.72 × 10²

e) 0.000984
Move decimal 4 places right:
9.84 × 10⁻⁴

f) 0.502
→ 5.02 × 10⁻¹

g) 3100.0 × 10²
First write 3100.0 in scientific notation:
3.1000 × 10³
Now multiply by 10² → 3.1000 × 10⁵
But since it’s already given as 3100.0 × 10², convert directly:
3.1000 × 10⁵

h) 0.0114 × 10⁴
Convert 0.0114 to scientific: 1.14 × 10⁻²
Then: (1.14 × 10⁻²) × 10⁴ = 1.14 × 10²

i) 107.2
→ 1.072 × 10²

j) 0.0000455
Move decimal 5 places right:
4.55 × 10⁻⁵

k) 2205.2
→ 2.2052 × 10³

l) 30.0 × 10⁻²
30.0 = 3.00 × 10¹
So: 3.00 × 10¹ × 10⁻² = 3.00 × 10⁻¹

m) 0.982 × 10⁻³
This is already close, but we need coefficient between 1 and 10:
0.982 = 9.82 × 10⁻¹
So: 9.82 × 10⁻¹ × 10⁻³ = 9.82 × 10⁻⁴

n) 0.0473
→ 4.73 × 10⁻²

o) 650,502
→ 6.50502 × 10⁵

p) 3.03 × 10⁻¹
Already in scientific notation: 3.03 × 10⁻¹

q) 20.4 × 10⁵
20.4 = 2.04 × 10¹
So: 2.04 × 10¹ × 10⁵ = 2.04 × 10⁶

r) 1000 × 10⁻³
1000 = 1 × 10³
So: 1 × 10³ × 10⁻³ = 1 × 10⁰ = 1

But in scientific notation: 1.0 × 10⁰

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✔ Answers for Part 1:

| Item | Scientific Notation |
|------|---------------------|
| a) | 3.427 × 10³ |
| b) | 4.56 × 10⁻³ |
| c) | 1.23453 × 10⁵ |
| d) | 1.72 × 10² |
| e) | 9.84 × 10⁻⁴ |
| f) | 5.02 × 10⁻¹ |
| g) | 3.1000 × 10⁵ |
| h) | 1.14 × 10² |
| i) | 1.072 × 10² |
| j) | 4.55 × 10⁻⁵ |
| k) | 2.2052 × 10³ |
| l) | 3.00 × 10⁻¹ |
| m) | 9.82 × 10⁻⁴ |
| n) | 4.73 × 10⁻² |
| o) | 6.50502 × 10⁵ |
| p) | 3.03 × 10⁻¹ |
| q) | 2.04 × 10⁶ |
| r) | 1.0 × 10⁰ |

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2. Determine the number of significant digits

Rules:
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Leading zeros (before first non-zero) are not significant.
- Trailing zeros are significant only if there's a decimal point or they are after a decimal.

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a) 3427
All digits non-zero → 4 sig figs

b) 0.00456
Leading zeros not significant → 456 → 3 sig figs

c) 123,453
All non-zero → 6 sig figs

d) 172
All non-zero → 3 sig figs

e) 0.000984
Only 984 → 3 sig figs

f) 0.502
5, 0 (between), 2 → all significant → 3 sig figs

g) 3100.0 × 10²
Number: 3100.0 → has decimal, so trailing zero counts → 3,1,0,0,0 → 5 sig figs

h) 0.0114 × 10⁴
Number: 0.0114 → leading zeros don’t count → 114 → 3 sig figs

i) 107.2
1, 0 (between), 7, 2 → all significant → 4 sig figs

j) 0.0000455
Only 455 → 3 sig figs

k) 2205.2
All digits significant → 5 sig figs

l) 30.0 × 10⁻²
30.0 → has decimal, trailing zero counts → 3, 0, 0 → 3 sig figs

m) 0.982 × 10⁻³
0.982 → leading zero doesn’t count → 9,8,2 → 3 sig figs

n) 0.0473
Leading zeros ignored → 473 → 3 sig figs

o) 650,502
All non-zero → 6 sig figs

p) 3.03 × 10⁻¹
3.03 → two zeros? No: 3, 0, 3 → zero is between → 3 sig figs

q) 20.4 × 10⁵
20.4 → 2, 0, 4 → zero between → 3 sig figs

r) 1000 × 10⁻³
1000 → no decimal → trailing zeros ambiguous, but typically 1 sig fig unless specified.
But here it's written as 1000 (no decimal), so only 1 sig fig

> Note: If it were 1000., it would be 4 sig figs, but without decimal, assume 1.

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✔ Answers for Part 2:

| Item | Sig Figs |
|------|----------|
| a) | 4 |
| b) | 3 |
| c) | 6 |
| d) | 3 |
| e) | 3 |
| f) | 3 |
| g) | 5 |
| h) | 3 |
| i) | 4 |
| j) | 3 |
| k) | 5 |
| l) | 3 |
| m) | 3 |
| n) | 3 |
| o) | 6 |
| p) | 3 |
| q) | 3 |
| r) | 1 |

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3. Convert each into decimal form

Use: $ a \times 10^n $ → move decimal point $ n $ places

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a) 1.56 × 10⁴
Move decimal 4 places right:
1.56 → 15600 → 15,600

b) 0.56 × 10⁻²
Move decimal 2 places left:
0.56 → 0.0056 → 0.0056

c) 3.69 × 10⁻²
Move 2 places left:
3.69 → 0.0369 → 0.0369

d) 736.9 × 10⁵
Move decimal 5 places right:
736.9 → 73,690,000 → 73,690,000

e) 0.00259 × 10⁵
First: 0.00259 → 2.59 × 10⁻³
Then: 2.59 × 10⁻³ × 10⁵ = 2.59 × 10² = 259
Or: 0.00259 × 100,000 = 259

f) 13.69 × 10⁻²
Move decimal 2 places left:
13.69 → 0.1369 → 0.1369

g) 6.9 × 10⁴
Move 4 places right:
6.9 → 69,000 → 69,000

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✔ Answers for Part 3:

| Item | Decimal Form |
|------|------------------|
| a) | 15,600 |
| b) | 0.0056 |
| c) | 0.0369 |
| d) | 73,690,000 |
| e) | 259 |
| f) | 0.1369 |
| g) | 69,000 |

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✔ Final Answers Summary:

#### 1. Scientific Notation
a) 3.427×10³
b) 4.56×10⁻³
c) 1.23453×10⁵
d) 1.72×10²
e) 9.84×10⁻⁴
f) 5.02×10⁻¹
g) 3.1000×10⁵
h) 1.14×10²
i) 1.072×10²
j) 4.55×10⁻⁵
k) 2.2052×10³
l) 3.00×10⁻¹
m) 9.82×10⁻⁴
n) 4.73×10⁻²
o) 6.50502×10⁵
p) 3.03×10⁻¹
q) 2.04×10⁶
r) 1.0×10⁰

#### 2. Significant Digits
a) 4
b) 3
c) 6
d) 3
e) 3
f) 3
g) 5
h) 3
i) 4
j) 3
k) 5
l) 3
m) 3
n) 3
o) 6
p) 3
q) 3
r) 1

#### 3. Decimal Form
a) 15,600
b) 0.0056
c) 0.0369
d) 73,690,000
e) 259
f) 0.1369
g) 69,000

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