powers on base 10 and their applications

To multiply by 10 we add a zero.

Example:  50 · 10=500

To calculate a power on base 10 we write 1 and as many zeros as the index.

Example: 10⁷ = 10.000.000

Polynomial decomposition is the decomposition in which each order of units is represented by a power on base 10.

Example:  
23.816 = 2 · 10⁴+ 3 · 10³ + 8 · 10² + 1 · 10 + 6

Exercises:

1.- Match these expressions:
a.10³                 A.One billion                              I)10.000.000
b.10⁷                 B.Ten hundreds                          II)1.000.000.000.000.000
c.10⁹                 C.One million thousands              III)1.000.000.000
d.10¹²                D.One thousand billion                IV)1.000
e.10¹⁵                E.Ten million                              V)1.000.000.000.000 

2.- Write the polynomial decomposition of these numbers:
a) 8531  
b) 305.020  
c) 92.475  

3.- Write the number which expresses each polynomial decomposition:
a) 7·10⁶+5·10⁴+1·10³+2·10²+8=
b) 1·10⁸+1·10⁶+3·10⁵+8·10²=

Solutions:

1.-  a-B-IV;b-E-I; c-C-III; d-A-V; e-D-II

2.-  a) 8·10³+5·10²+3·10+1; b) 3·10⁵+5·10³+2·10; c) 9·10⁴+2·10³+4·10²+7·10+5

3.- a) 7.051.208; b) 101.300.800