Operations with Scientific Notation — Practice
Handle the front numbers and the powers of ten separately, then tidy the result back into proper form.
What these questions cover
These questions use 4 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Rate — A ratio of two different units, like miles per hour or dollars per pound.
- Exponent — How many times the base is used as a factor. In 53 the exponent is 3.
- Scientific notation — A number written as a × 10n, where 1 ≤ a < 10.
- Standard form — The ordinary way of writing a number, like 47,000.
Problem 1
Write 47,000 in scientific notation.
Worked answer
4.7 x 10^4
4.7, moved 4 places
4.7 × 104
Problem 2
Write 0.00062 in scientific notation.
Worked answer
6.2 x 10^-4
6.2, moved 4 places right
6.2 × 10-4
Problem 3
Write 3.5 × 105 in standard form.
Worked answer
350000
350,000
Problem 4
Compute (2 × 103)(4 × 105).
Worked answer
8 x 10^8
2 × 4 = 8
3 + 5 = 8
8 × 108
Problem 5
Compute 9 × 1073 × 102.
Worked answer
3 x 10^5
9 ÷ 3 = 3
7 - 2 = 5
3 × 105
Problem 6
Compute (5 × 104)(6 × 103) in proper scientific notation.
Worked answer
3 x 10^8
5 × 6 = 30 and 4 + 3 = 7
30 × 107 — front is too big
= 3 × 108
Problem 7
Compute (8 × 10-3)(2 × 106).
Worked answer
1.6 x 10^4
8 × 2 = 16
-3 + 6 = 3
16 × 103 = 1.6 × 104
Problem 8
Compute 4.5 × 106 + 2 × 106.
Worked answer
6.5 x 10^6
4.5 + 2 = 6.5
6.5 × 106
Problem 9
Compute 8 × 105 + 3 × 104.
Worked answer
8.3 x 10^5
3 × 104 = 0.3 × 105
8 + 0.3 = 8.3
8.3 × 105
Problem 10
Which is larger, 3 × 108 or 9 × 107?
- 3 × 108
- 9 × 107
- They are equal
- Cannot be determined
Worked answer
3 × 108
108 > 107
3 × 108 = 300,000,000
9 × 107 = 90,000,000
Problem 11
How many times larger is 6 × 109 than 2 × 106?
Worked answer
3000
6 ÷ 2 = 3
109 ÷ 106 = 103
3 × 103 = 3000
Problem 12
Rewrite 0.045 × 107 in proper scientific notation.
Worked answer
4.5 x 10^5
0.045 = 4.5 × 10-2
-2 + 7 = 5
4.5 × 105
Problem 13
Compute 7.2 × 108 - 4 × 107.
Worked answer
6.8 x 10^8
4 × 107 = 0.4 × 108
7.2 - 0.4 = 6.8
6.8 × 108
Problem 14
A virus is 1.2 × 10-7 m across; a cell is 3 × 10-5 m. How many times wider is the cell?
Worked answer
250
3 ÷ 1.2 = 2.5
10-5 ÷ 10-7 = 102
2.5 × 102 = 250 times
Problem 15
Compute 2 × 1048 × 10-2 in scientific notation.
Worked answer
2.5 x 10^5
2 ÷ 8 = 0.25
4 - (-2) = 6
0.25 × 106 = 2.5 × 105
Problem 16
Light travels 3 × 108 m/s. How far does it travel in 2 × 103 seconds?
Worked answer
6 x 10^11
3 × 2 = 6
8 + 3 = 11
6 × 1011 metres