Standard Form Notation
Negative Indices and Standard form - part 1
Follow the examples below:
| a) |
52000 = 5.2 * 104 |
| b) |
5200 = 5.2 * 103 |
| c) |
520 = 5.2 * 102 |
| d) |
52 = 5.2 * 101 |
| e) |
5.2 = 5.2 * 100 |
| f) |
0.52 = 5.2 * 10-1 |
| g) |
0.052 = 5.2 * 10-2 |
| i) |
0.0052 = 5.2 * 10-3 |
Looking at the pattern of indices we reduce by one each step: 4, 3, 2,
1, 0, -1, -2, -3 etc.
A negative index means in those cases:
To get the standard form, the decimal point has moved one place to the right.
To get the standard form, the decimal point has moved 2 places
to the right.
To get the standard form, the decimal point has moved 3 places
to the right.
Definition
A move of the decimal point to the right tells us that we dividing by
factors of 10, not multiplying.
| 104 |
103 |
102 |
101 |
100 |
10-1 |
10-2 |
10-3 |
| Ten Thousands |
Thousands |
Hundreds |
Tens |
Ones |
Tenths |
Hundreds |
Thousandths |
| 10000 |
1000 |
100 |
10 |
1 |
1/10 |
1/100 |
1/1000 |
The decimal system of writing numbers goes both ways. Going from large
numbers to small numbers (left, right) notice the power goes down by one
each time. We use 10-1 (10 to the power -1) to mean 1 tenth
(1/10) or 0.1. Similarly 10-2 means 1 hundredth (1/100) or 0.01;
10-3 means thousand (1/1000) or 0.001.
Exercise 1
Write the following numbers as ordinary decimals:
a) 5 * 10-4
Solution: 5 * 10-4 = 5/10000 = 0.0005
5 * 10-4 means 5/10000 or 0.0005 a move of the decimal point
to the right tells us that we are dividing by the power of 10.
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