Question

Compare: 0.06 x 10-1 O 10-2A>B)

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given question.

$0.06\times10^{-1}O\text{ }0.6\times10^{-2}$

STEP 2: Divide the expression into two parts and solve each parts to get their results

$\begin{gathered} 0.06\times10^{-1}\Rightarrow\text{?} \\ 0.6\times10^{-2}\Rightarrow\text{?} \end{gathered}$

STEP 3: Solve the first expression

$\begin{gathered} 0.06\times10^{-1} \\ 0.06\times10^{-1} \\ =0.06\times\frac{1}{10} \\ \mathrm{Multiply\: fractions}\colon\quad \: a\times\frac{b}{c}=\frac{a\:\times\:b}{c} \\ =\frac{1\times\:0.06}{10} \\ \mathrm{Multiply\: the\: numbers\colon}\: 1\times\: 0.06=0.06 \\ =\frac{0.06}{10} \\ \mathrm{Divide\: the\: numbers\colon}\: \frac{0.06}{10}=0.006 \\ =0.006 \end{gathered}$

STEP 4: Solve the second expression

$\begin{gathered} 0.6\times10^{-2} \\ \mathrm{Apply\: exponent\: rule}\colon\quad \: a^{-b}=\frac{1}{a^b} \\ \mathrm{Multiply\: fractions}\colon\quad \: a\times\frac{b}{c}=\frac{a\:\times\:b}{c} \\ =\frac{1\times\:0.6}{10^2} \\ \mathrm{Multiply\: the\: numbers\colon}\: 1\times\: 0.6=0.6 \\ =\frac{0.6}{10^2} \\ 10^2=100 \\ =\frac{0.6}{100} \\ \mathrm{Divide\: the\: numbers\colon}\: \frac{0.6}{100}=0.006 \\ =0.006 \end{gathered}$

STEP 5: Compare the two results from the simplified expressions

$\begin{gathered} \text{0}.006\Rightarrow0.006 \\ It\text{ can be se}en\text{ that the expression on the right hand side is equal to the expression on the left hand side} \end{gathered}$

Hence,

$0.06\times10^{-1}=\text{ }0.6\times10^{-2}$

Equal sign(=)