Theory:

Repeat!
 
Grade 
Solution 
The value of the step
103 =10 ·10 ·10\(= 1000\)
102 =10 ·10\(= 100\)
101 =any number in the first degree
is equal to itself
\(= 10\)
100 =any number in the zero degree
is equal to 1
\(= 1\)
101 =1101=110\(= 0.1\)
102 =1102=11010=1100\(= 0.01\)
103 =1103=1101010=11000\(= 0.001\)
 
an=1an
 
To record very large or very small numbers, use the normal form.
The normal form of a number is called the multiple of this number: a10nwhere1a<10
Note that greater than \(1\) and less than \(10.\)
 
If the number is greater than or equal to \(10,\) then writes in normal form \(10\) with a positive lever,
for example, blue whale mass is approx 1.9 ·105\(kg\).
 
If the number is less than \(1,\) then writes in normal form \(10\) with a negative gain,
for example, the mass of the smallest ants is approx \(0.000001 kg =\) 1106 \(kg\).
 
Remember that an integer is after the last digit.
\(1 = 1.0 \)\(300 = 300.0 \)\(50,000 = 50,000.0\)
\(20 = 20.0\)\(4000 = 4000.0 \)\(600,000 = 600,\)\(000.0\)
 
Important!
When switching from a number to a normal notation (or vice versa), move the period to the right or left in the number and multiply it by \(10\) the appropriate degree.
If the normal format is to write a number greater than \(10,\) then move the period to the left.
Example:
\(98765 =\) 9.8765 ·104
Period moved \(4\) places to the left.
9.8765.0
 
\( 12345600 =\) 1.23456 ·107
 
Period moved \(7\) places to the left.
1.2345600.0
If the normal form is to write a number smaller than \(1,\) then move the period to the right.
Example:
\(0.012345 =\) 1.2345102
Period moved \(2\) places to the right.
0.01.2345
 
\(0.00234567 =\)  2.34567103
 
Period moved \(3\) places to the right.
0.002.34567
 
\(0.000789 =\)7.89104
 
Period moved \(4\) places to the right.
0.0007.89
Reference:
Mathematics for 7th grade / Ilze France, Gunta Lace, Ligita Pickaine, Anita Mikelsone. - Lielvarde: Lielvārde, 2007. - 248 pp. - References: 119-120. p.