Operations with Scientific Notation — Drills
Operations with Scientific Notation has 10 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills 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.
Converting units
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write 0.000087 in scientific notation.
Worked answer
8.7 x 10^-5
Front number: 8.7
Moved 5 places right
8.7 × 10-5
Problem 2
Write 18,000 in scientific notation.
Worked answer
1.8 x 10^4
Front number: 1.8
Moved 4 places left
1.8 × 104
Multiplying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Compute (6 × 108)(6 × 101) in scientific notation.
Worked answer
3.6 x 10^10
6 × 6 = 36
8 + (1) = 9
36 × 109 = 3.6 × 1010
Problem 2
Compute (8 × 101)(5 × 10-2) in scientific notation.
Worked answer
4 x 10^0
8 × 5 = 40
1 + (-2) = -1
40 × 10-1 = 4 × 100
Dividing
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Compute 12 × 1043 × 101.
Worked answer
4 x 10^3
12 ÷ 3 = 4
4 - (1) = 3
4 × 103
Problem 2
Compute 15 × 10-35 × 10-2.
Worked answer
3 x 10^-1
15 ÷ 5 = 3
-3 - (-2) = -1
3 × 10-1
Tidy
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Compute (9 × 102)(8 × 100) in proper scientific notation.
Worked answer
7.2 x 10^3
9 × 8 = 72
72 × 102 — the front is too big
= 7.2 × 103
Problem 2
Compute (4 × 107)(7 × 100) in proper scientific notation.
Worked answer
2.8 x 10^8
4 × 7 = 28
28 × 107 — the front is too big
= 2.8 × 108
Adding
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Compute 2.8 × 106 + 7 × 106.
Worked answer
9.8 x 10^6
2.8 + 7 = 9.8
9.8 × 106
Problem 2
Compute 4.6 × 103 + 6 × 102.
Worked answer
5.2 x 10^3
6 × 102 = 0.6 × 103
4.6 + 0.6 = 5.2
5.2 × 103
Subtracting
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Compute 6.9 × 109 - 6 × 108.
Worked answer
6.3 x 10^9
6 × 108 = 0.6 × 109
6.9 - 0.6 = 6.3
6.3 × 109
Problem 2
Compute 8.2 × 106 - 4 × 105.
Worked answer
7.8 x 10^6
4 × 105 = 0.4 × 106
8.2 - 0.4 = 7.8
7.8 × 106
Comparing
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which is larger, 8 × 104 or 6 × 101?
- Cannot be determined
- 8 × 104
- 6 × 101
- They are equal
Worked answer
8 × 104
104 > 101
A bigger exponent wins whatever the front numbers are.
So 8 × 104.
Problem 2
Which is larger, 2 × 108 or 5 × 105?
- 2 × 108
- They are equal
- 5 × 105
- Cannot be determined
Worked answer
2 × 108
108 > 105
A bigger exponent wins whatever the front numbers are.
So 2 × 108.
Howmany
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
How many times larger is 24 × 106 than 6 × 103?
Worked answer
4000
24 ÷ 6 = 4
106 ÷ 103 = 103
4 × 1000 = 4000
Problem 2
How many times larger is 6 × 108 than 2 × 105?
Worked answer
3000
6 ÷ 2 = 3
108 ÷ 105 = 103
3 × 1000 = 3000
Fix
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Rewrite 0.03 × 108 in proper scientific notation.
Worked answer
3 x 10^6
0.03 = 3 × 10-2
-2 + 8 = 6
3 × 106
Problem 2
Rewrite 0.051 × 107 in proper scientific notation.
Worked answer
5.1 x 10^5
0.051 = 5.1 × 10-2
-2 + 7 = 5
5.1 × 105
Word problems
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A signal travels 8 × 105 metres per second. How far does it go in 6 × 103 seconds?
Worked answer
4.8 x 10^9
8 × 6 = 48
5 + 3 = 8
4.8 × 109 metres
Problem 2
A signal travels 2 × 108 metres per second. How far does it go in 5 × 102 seconds?
Worked answer
1 x 10^11
2 × 5 = 10
8 + 2 = 10
1 × 1011 metres