Question

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

Answer 1

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

STEP 1: Write the given question.

`0.06*10^(-1)O\text{ }0.6*10^(-2)`

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

`\begin{gathered} 0.06*10^(-1)\Rightarrow\text{?} \\ 0.6*10^(-2)\Rightarrow\text{?} \end{gathered}`

STEP 3: Solve the first expression

`\begin{gathered} 0.06*10^(-1) \\ 0.06*10^(-1) \\ =0.06*(1)/(10) \\ \mathrm{Multiply\: fractions}\colon\quad \: a*(b)/(c)=(a\:*\:b)/(c) \\ =(1*\:0.06)/(10) \\ \mathrm{Multiply\: the\: numbers\colon}\: 1*\: 0.06=0.06 \\ =(0.06)/(10) \\ \mathrm{Divide\: the\: numbers\colon}\: (0.06)/(10)=0.006 \\ =0.006 \end{gathered}`

STEP 4: Solve the second expression

`\begin{gathered} 0.6*10^(-2) \\ \mathrm{Apply\: exponent\: rule}\colon\quad \: a^(-b)=(1)/(a^b) \\ \mathrm{Multiply\: fractions}\colon\quad \: a*(b)/(c)=(a\:*\:b)/(c) \\ =(1*\:0.6)/(10^2) \\ \mathrm{Multiply\: the\: numbers\colon}\: 1*\: 0.6=0.6 \\ =(0.6)/(10^2) \\ 10^2=100 \\ =(0.6)/(100) \\ \mathrm{Divide\: the\: numbers\colon}\: (0.6)/(100)=0.006 \\ =0.006 \end{gathered}`

STEP 5: Compare the two results from the simplified expressions

Hence,

`0.06*10^(-1)=\text{ }0.6*10^(-2)`

Equal sign(=)