Question

Expand the following using exponents. (i) 0.0523 (ii) 32.005

Answer 1

Answer:

1)$0.0523 =5*10^{-1} + 2*10x^{-2} + 3*10x^{-3} \\32.005 =3*10^{1} +2*10x^{0} + 5*10x^{-3}$

Answer 2

Given:

(i) 0.0523 (ii) 32.005

To find:

The expanded form of given decimals using exponents.

Solution:

(i) 0.0523

The place value of 5 is

$\frac{5}{100} = 5 \times {10}^{ - 2}$

Similarly,

the place value of 2 is

$\frac{2}{1000} = 2 \times {10}^{ - 3}$the place value of 3 is

$\frac{3}{10000} = 3 \times {10}^{ - 4}$

So,

The expanded form of 0.0523 is

$= 5 \times {10}^{ - 2} + 2 \times {10}^{ - 3} + 3 \times {10}^{ - 4}$

(ii) 32.005

The given decimal number 32.005 can be written as 32 + 0.005

Now,

Proceeding same as in (i),

the place value of 3 is

$30 = 3 \times {10}^{1}$

The place value of 2 is

$2 = 2 \times {10}^{0}$

The place value of 5 is

$\frac{5}{1000} = 5 \times {10}^{ - 3}$

So,

The expanded form of 32.005 is

$3 \times {10}^{1} + 2 \times {10}^{0} + 5 \times {10}^{ - 3}$