Let's solve each problem step by step.
---
Part 1: Write each number in scientific notation
Scientific notation is written as:
$$ a \times 10^n $$
where $1 \leq |a| < 10$ and $n$ is an integer.
---
1)
0.000055
Move the decimal point to the right until you get a number between 1 and 10:
0.000055 → 5.5 (moved 5 places to the right)
So, $ 5.5 \times 10^{-5} $
✔ Answer: $ 5.5 \times 10^{-5} $
2)
225,000
Move the decimal point to the left:
225,000 → 2.25 (moved 5 places to the left)
So, $ 2.25 \times 10^5 $
✔ Answer: $ 2.25 \times 10^5 $
3)
0.00179
Move decimal to the right:
0.00179 → 1.79 (moved 3 places)
So, $ 1.79 \times 10^{-3} $
✔ Answer: $ 1.79 \times 10^{-3} $
4)
18,569
Move decimal to the left:
18,569 → 1.8569 (moved 4 places)
So, $ 1.8569 \times 10^4 $
✔ Answer: $ 1.8569 \times 10^4 $
5)
41,214
→ 4.1214 × 10⁴ (moved 4 places left)
✔ Answer: $ 4.1214 \times 10^4 $
6)
2,276
→ 2.276 × 10³
✔ Answer: $ 2.276 \times 10^3 $
7)
0.000207
→ 2.07 × 10⁻⁴ (moved 4 places right)
✔ Answer: $ 2.07 \times 10^{-4} $
8)
0.00939
→ 9.39 × 10⁻³
✔ Answer: $ 9.39 \times 10^{-3} $
9)
5.5 × 10⁵
This is already in scientific notation.
✔ Answer: $ 5.5 \times 10^5 $ (no change)
10)
8.2 × 10⁻⁴
Also already in scientific notation.
✔ Answer: $ 8.2 \times 10^{-4} $
---
Part 2: Write each number in standard form
Now convert from scientific notation to standard (decimal) form.
---
11)
1.0018 × 10¹¹
Move decimal 11 places to the right:
1.0018 → 100,180,000,000
(Add 11 zeros, but account for digits after decimal)
→ 100,180,000,000
✔ Answer: 100,180,000,000
12)
7.754 × 10⁻⁴
Move decimal 4 places to the
left:
7.754 → 0.0007754
✔ Answer: 0.0007754
13)
5.462 × 10⁴
Move decimal 4 places right:
5.462 → 54,620
✔ Answer: 54,620
14)
7.973 × 10²
Move decimal 2 places right:
7.973 → 797.3
✔ Answer: 797.3
15)
6.06 × 10⁶
Move decimal 6 places right:
6.06 → 6,060,000
✔ Answer: 6,060,000
16)
4.11 × 10³
Move decimal 3 places right:
4.11 → 4,110
✔ Answer: 4,110
17)
4.571 × 10⁴
Move decimal 4 places right:
4.571 → 45,710
✔ Answer: 45,710
18)
9.5 × 10⁵
Move decimal 5 places right:
9.5 → 950,000
✔ Answer: 950,000
19)
2.614 × 10⁶
Move decimal 6 places right:
2.614 → 2,614,000
✔ Answer: 2,614,000
20)
4 × 10⁻⁶
Move decimal 6 places to the left:
4 → 0.000004
✔ Answer: 0.000004
---
✔ Final Answers:
####
Scientific Notation:
1) $ 5.5 \times 10^{-5} $
2) $ 2.25 \times 10^5 $
3) $ 1.79 \times 10^{-3} $
4) $ 1.8569 \times 10^4 $
5) $ 4.1214 \times 10^4 $
6) $ 2.276 \times 10^3 $
7) $ 2.07 \times 10^{-4} $
8) $ 9.39 \times 10^{-3} $
9) $ 5.5 \times 10^5 $
10) $ 8.2 \times 10^{-4} $
####
Standard Form:
11) 100,180,000,000
12) 0.0007754
13) 54,620
14) 797.3
15) 6,060,000
16) 4,110
17) 45,710
18) 950,000
19) 2,614,000
20) 0.000004
---
Let me know if you'd like this formatted as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of scientific notation worksheet for 8th grade.
