Consider the following facts
1) 3 ×10 ×10 ×10 ×10 ×10 ×10 =3000000
2) 3.6 ×10 ×10 ×10 =3600
3)2.76×10 ×10 ×10 ×10 27600
We can rewrite each of these as
1) 3000000 = 3.0 × 10 6 ( ie multiplied by 6 tens)
2) 3600 = 3.6 × 10 3 (ie multiplied by 3 tens)
3) 27600 = 2.76 × 10 4 (ie multiplied by 4 tens)
These are called STANDARD FORM)
1) 3.15 × 10 6 = 3150000 (3.15 multiplied by 10, six times)
2) 1.02 × 10 4 = 10200 (1.02 multiplied by 10, four times)
3) 5.234 × 10 2 = 523.4 (5.234 multiplied by 10, two times)
4) 4.001 × 10 1 = 10.01 (4.001 multiplied by 10, one time)
1) To write 31000 in standard form. We observe that 31000 = 3.1000 ×10 ×10 ×10 ×10
31000 = 3.1000 ×10 4 = 3.1 ×10 4
2) To write 213000 in standard form. We observe that 213000 = 2.13000 ×10 ×10 ×10 ×10 ×l10
213000 = 2.13000 ×10 5 = 2.13 ×10 5
3) To write 31000.5 in standard form. We observe that 31000.5 = 3.10005 ×10 ×10 ×10 ×10
31000.5 = 3.10005 ×10 4
The POWER of 10 required, is always the number of digits between the first digit in the number and the decimal place
Comnsider the following facts:
1) 0.0005 = 5 × 10 -4 (Divided by 10, four times)
2) 0.0025 = 2.5 × 10 -4 (Divided by 10, four times)
3) 0.000013 = 1.3 × 10 -5 (Divided by 10, five times)
This is standard form involving negative powers
1) 0.00007 = 7 ÷10 ÷10 ÷10 ÷10 ÷10 = 7 × 10 -5
2) 0.0000013 = 1.3 ÷10 ÷10 ÷10 ÷10 ÷10 ÷10 = 1.3 × 10 -6
3) 0.000000010001 = 1.0001 ÷10 ÷10 ÷10 ÷10 ÷10 ÷10 ÷10 ÷10 = 1.0001 × 10 -8
The number required in the power of 10 is equal to the number of digits between the decimal point and the first non-zero digit inclusive