Question

Expand the following numbers using exponents:

a) $1029.63$

b) $1296.249$

Answer 1

$\begin{array}{ccccccc}\text{Thousands}\left({10}^3\right)& \text{Hunderds}\left({10}^2\right)& \text{Tens}\left({10}^1\right)& \text{Ones}({10}^0=1)& \text{Tenths}(\frac{1}{10}={10}^{-1})& \text{Hundredths}(\frac{1}{100}={10}^{-2})& \text{Thousandths}(\frac{1}{1000}={10}^{-3})\\ 1& 0& 2& 9& 6& 3& \\ 1& 2& 9& 6& 2& 4& 9\end{array}$

$a)1029.63=1\times {10}^3+0\times {10}^2+2\times {10}^1+9\times {10}^0+6\times {10}^{-1}+3\times {10}^{-2}$

$=1000+0+20+9+\frac{6}{10}+\frac{3}{100}$

$b)1296.249=1\times {10}^3+2\times {10}^2+9\times {10}^1+6\times {10}^0+2\times {10}^{-1}+4\times {10}^{-2}+9\times {10}^{-3}$

$=1000+200+9+6+\frac{2}{10}+\frac{4}{100}+\frac{9}{1000}$