Laws of integral indices · Ages 13–14
Scientific notation
a × 10n with 1 ≤ a < 10; the point moved left, index positive; right, negative.
How to do it
Method
a × 10^n with 1 ≤ a < 10; the point moved left, index positive; right, negative
3,400,000 = 3.4 × 106; 0.00052 = 5.2 × 10−4
Another way
Front numbers and powers apart
(3 × 104) × (5 × 103) = 15 × 107 = 1.5 × 108
In full
Scientific notation writes a number as a × 10n, where 1 ≤ a < 10 and n is a whole number. A big number: move the point of 3,400,000 six places left to get 3.4, so 3,400,000 = 3.4 × 106. A small one: move the point of 0.00052 four places right to get 5.2, so 0.00052 = 5.2 × 10−4. The point moved left gives a positive index; moved right, a negative one. To calculate, work the front numbers and the powers of 10 apart: (3 × 104) × (5 × 103) = 15 × 107, but 15 isn't between 1 and 10, so adjust it to 1.5 × 108. Dividing is the same: (8 × 106) ÷ (2 × 109) = 4 × 10−3. To compare, compare the indices of 10 first. Or write the numbers out in full and work with them: the same answer, though zeros are easier to miscount.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
In scientific notation: (7 × 105) × (9 × 104) = × 10□
Fill in each blank
Show the answer and working
Answer: 6.3, 10
7 × 9 = 63 and 105 × 104 = 10^(5 + 4); the front number must be from 1 to under 10, so adjust: 6.3 × 1010.
Example 2
In scientific notation: (4 × 10−1) ÷ (8 × 104) = × 10□
Fill in each blank
Show the answer and working
Answer: 5, −6
4 ÷ 8 = 0.5 and 10−1 ÷ 104 = 10^(−1 − (4)); the front number must be from 1 to under 10, so adjust: 5 × 10−6.
Example 3
Which number is the largest?
- A. 4.8 × 107
- B. 4.6 × 103
- C. 4.3 × 106
- D. 3.7 × 106
Choose the right answer
Show the answer and working
Answer: A. 4.8 × 107
The bigger index of 10 wins; with equal indices, the bigger front number.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.As an ordinary number: 3.7 × 105 =
Answer:
2.9.9 × 107 is a number in scientific notation.
True or false?
Answer:
3.What is 6,700,000 in scientific notation?
- A. 6.7 × 106
- B. 67 × 105
- C. 6.7 × 107
- D. 6.7 × 10−6
Choose the right answer
Answer:
4.In scientific notation: 140 = × 10□
Fill in each blank
Answer:
5.In scientific notation: (7 × 107) × (9 × 107) = × 10□
Fill in each blank
Answer:
All the answers
- 1. 370000
- 2. True
- 3. A. 6.7 × 106
- 4. 1.4, 2
- 5. 6.3, 15
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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