Scientific Notation worksheet

1. Decimal form: 6,000,000,000,000,000,000,000,000

1. Multiplying by 10 to the power 24 moves the decimal point 24 places to the right, adding zeros as needed

   $\text{6}\times {10}^{24}$$=\text{6,000,000,000,000,000,000,000,000}$

2. Decimal form: 5,250,000,000,000,000,000

1. Multiplying by 10 to the power 18 moves the decimal point 18 places to the right, adding zeros as needed

   $\text{5.25}\times {10}^{18}$$=\text{5,250,000,000,000,000,000}$

3. Scientific notation: 2.7500 × 10⁸

1. Move the decimal point 8 places to the left, so just one digit that isn't zero sits in front of it. The count of moves gives the power of ten: 8

   $\text{275,000,000}$$=\text{2.75}\times {10}^8$

2. Round the number in front so it keeps 5 digits that count. If the next digit is 5 or more, round up, away from zero

   $\text{2.75}\times {10}^8$$=\text{2.7500 × 10⁸}$

3. For the engineering form, shift the point so the power of ten is a multiple of 3. That way it lines up with kilo, mega and the other metric prefixes

   $\text{2.7500 × 10⁸}$$=\text{275.00 × 10⁶}$

4. Scientific notation: 3.6000 × 10⁸

1. Move the decimal point 8 places to the left, so just one digit that isn't zero sits in front of it. The count of moves gives the power of ten: 8

   $\text{360,000,000}$$=\text{3.6}\times {10}^8$

2. Round the number in front so it keeps 5 digits that count. If the next digit is 5 or more, round up, away from zero

   $\text{3.6}\times {10}^8$$=\text{3.6000 × 10⁸}$

3. For the engineering form, shift the point so the power of ten is a multiple of 3. That way it lines up with kilo, mega and the other metric prefixes

   $\text{3.6000 × 10⁸}$$=\text{360.00 × 10⁶}$

5. Scientific notation: 2.800 × 10⁸

1. Move the decimal point 8 places to the left, so just one digit that isn't zero sits in front of it. The count of moves gives the power of ten: 8

   $\text{280,000,000}$$=\text{2.8}\times {10}^8$

2. Round the number in front so it keeps 4 digits that count. If the next digit is 5 or more, round up, away from zero

   $\text{2.8}\times {10}^8$$=\text{2.800 × 10⁸}$

3. For the engineering form, shift the point so the power of ten is a multiple of 3. That way it lines up with kilo, mega and the other metric prefixes

   $\text{2.800 × 10⁸}$$=\text{280.0 × 10⁶}$

6. Scientific notation: 2.5000 × 10⁸

1. Move the decimal point 8 places to the left, so just one digit that isn't zero sits in front of it. The count of moves gives the power of ten: 8

   $\text{250,000,000}$$=\text{2.5}\times {10}^8$

2. Round the number in front so it keeps 5 digits that count. If the next digit is 5 or more, round up, away from zero

   $\text{2.5}\times {10}^8$$=\text{2.5000 × 10⁸}$

3. For the engineering form, shift the point so the power of ten is a multiple of 3. That way it lines up with kilo, mega and the other metric prefixes

   $\text{2.5000 × 10⁸}$$=\text{250.00 × 10⁶}$

7. Scientific notation: 4.50000 × 10⁸

1. Move the decimal point 8 places to the left, so just one digit that isn't zero sits in front of it. The count of moves gives the power of ten: 8

   $\text{450,000,000}$$=\text{4.5}\times {10}^8$

2. Round the number in front so it keeps 6 digits that count. If the next digit is 5 or more, round up, away from zero

   $\text{4.5}\times {10}^8$$=\text{4.50000 × 10⁸}$

3. For the engineering form, shift the point so the power of ten is a multiple of 3. That way it lines up with kilo, mega and the other metric prefixes

   $\text{4.50000 × 10⁸}$$=\text{450.000 × 10⁶}$

8. Scientific notation: 3.600 × 10⁸

1. Move the decimal point 8 places to the left, so just one digit that isn't zero sits in front of it. The count of moves gives the power of ten: 8

   $\text{360,000,000}$$=\text{3.6}\times {10}^8$

2. Round the number in front so it keeps 4 digits that count. If the next digit is 5 or more, round up, away from zero

   $\text{3.6}\times {10}^8$$=\text{3.600 × 10⁸}$

3. For the engineering form, shift the point so the power of ten is a multiple of 3. That way it lines up with kilo, mega and the other metric prefixes

   $\text{3.600 × 10⁸}$$=\text{360.0 × 10⁶}$

9. Decimal form: 5,500,000,000,000,000,000

1. Multiplying by 10 to the power 18 moves the decimal point 18 places to the right, adding zeros as needed

   $\text{5.5}\times {10}^{18}$$=\text{5,500,000,000,000,000,000}$

10. Decimal form: 6,000,000,000,000,000,000

1. Multiplying by 10 to the power 18 moves the decimal point 18 places to the right, adding zeros as needed

   $\text{6}\times {10}^{18}$$=\text{6,000,000,000,000,000,000}$