Let’s solve each problem step by step. Scientific notation means writing a number as:
a × 10ⁿ
where:
-
a is a number between 1 and 10 (including 1, but less than 10)
-
n is an integer (positive or negative)
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For small numbers (less than 1):
Move the decimal point to the right until you have a number between 1 and 10. Count how many places you moved — that’s your negative exponent.
Example:
0.000075 → move decimal 5 places right → 7.5 → so it’s
7.5 × 10⁻⁵
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For large numbers (greater than 10):
Move the decimal point to the left until you have a number between 1 and 10. Count how many places you moved — that’s your positive exponent.
Example:
4,523,000 → move decimal 6 places left → 4.523 → so it’s
4.523 × 10⁶
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Now let’s do all 18 problems one by one.
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1) 0.000075
→ Move decimal 5 places right → 7.5
→ Answer:
7.5 × 10⁻⁵
2) 0.00005
→ Move decimal 5 places right → 5.0
→ Answer:
5 × 10⁻⁵
3) 0.000022
→ Move decimal 5 places right → 2.2
→ Answer:
2.2 × 10⁻⁵
4) 0.017
→ Move decimal 2 places right → 1.7
→ Answer:
1.7 × 10⁻²
5) 4,523,000
→ Move decimal 6 places left → 4.523
→ Answer:
4.523 × 10⁶
6) 83.6
→ Move decimal 1 place left → 8.36
→ Answer:
8.36 × 10¹
7) 990
→ Move decimal 2 places left → 9.9
→ Answer:
9.9 × 10²
8) 325
→ Move decimal 2 places left → 3.25
→ Answer:
3.25 × 10²
9) 8,600
→ Move decimal 3 places left → 8.6
→ Answer:
8.6 × 10³
10) 75,000
→ Move decimal 4 places left → 7.5
→ Answer:
7.5 × 10⁴
11) 127.8
→ Move decimal 2 places left → 1.278
→ Answer:
1.278 × 10²
12) 5,962
→ Move decimal 3 places left → 5.962
→ Answer:
5.962 × 10³
13) 1.76
→ Already between 1 and 10 → no move needed
→ Answer:
1.76 × 10⁰ (or just 1.76, but scientific notation usually includes ×10⁰ for consistency)
*Note: Some teachers accept 1.76 without the exponent, but strictly speaking, scientific notation requires the power of 10. So we’ll write 1.76 × 10⁰.*
14) 0.0000001901
→ Move decimal 7 places right → 1.901
→ Answer:
1.901 × 10⁻⁷
15) 9,110
→ Move decimal 3 places left → 9.11
→ Answer:
9.11 × 10³
16) 3,800
→ Move decimal 3 places left → 3.8
→ Answer:
3.8 × 10³
17) 80,400
→ Move decimal 4 places left → 8.04
→ Answer:
8.04 × 10⁴
18) 4.8
→ Already between 1 and 10 → no move needed
→ Answer:
4.8 × 10⁰
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✔ Double-checked all answers — exponents match decimal moves, coefficients are between 1 and 10.
Final Answer:
1) 7.5 × 10⁻⁵
2) 5 × 10⁻⁵
3) 2.2 × 10⁻⁵
4) 1.7 × 10⁻²
5) 4.523 × 10⁶
6) 8.36 × 10¹
7) 9.9 × 10²
8) 3.25 × 10²
9) 8.6 × 10³
10) 7.5 × 10⁴
11) 1.278 × 10²
12) 5.962 × 10³
13) 1.76 × 10⁰
14) 1.901 × 10⁻⁷
15) 9.11 × 10³
16) 3.8 × 10³
17) 8.04 × 10⁴
18) 4.8 × 10⁰
Parent Tip: Review the logic above to help your child master the concept of scientific notation practice problems worksheet.
