Write these numbers in order of size, starting with the smallest number.

[tex]\[ 71.8\% \quad \frac{11}{16} \quad \frac{5}{7} \quad 0.71 \][/tex]



Answer :

Certainly! To determine the order of the given numbers from smallest to largest, we first need to convert all of these numbers into a comparable format.

1. 71.8%: Convert the percentage to a decimal by dividing by 100.
[tex]\[ 71.8\% = \frac{71.8}{100} = 0.718 \][/tex]

2. \(\frac{11}{16}\): Keep this in its fractional form but convert it to a decimal for easy comparison.
[tex]\[ \frac{11}{16} \approx 0.6875 \][/tex]

3. \(\frac{5}{7}\): Again, this fraction needs to be converted to a decimal.
[tex]\[ \frac{5}{7} \approx 0.7143 \][/tex]

4. 0.71: This number is already given in decimal form.

Now we have the following numbers in decimal form:
[tex]\[ 0.718, \quad 0.6875, \quad 0.7143, \quad 0.71 \][/tex]

Next, we will arrange these decimals from smallest to largest:
\begin{itemize}
\item 0.6875 (which is \(\frac{11}{16}\))
\item 0.71
\item 0.7143 (which is \(\frac{5}{7}\))
\item 0.718 (which is 71.8%)
\end{itemize}

So, in order of size, starting with the smallest number:
[tex]\[ \frac{11}{16}, \quad 0.71, \quad \frac{5}{7}, \quad 71.8\% \][/tex]

Step-by-step explanation:

Certainly! To determine the order of the given numbers from smallest to largest, we first need to convert all of these numbers into a comparable format.

1. 71.8%: Convert the percentage to a decimal by dividing by 100.

71.8

%

=

71.8

100

=

0.718

71.8%=

100

71.8

=0.718

2. \(\frac{11}{16}\): Keep this in its fractional form but convert it to a decimal for easy comparison.

11

16

0.6875

16

11

≈0.6875

3. \(\frac{5}{7}\): Again, this fraction needs to be converted to a decimal.

5

7

0.7143

7

5

≈0.7143

4. 0.71: This number is already given in decimal form.

Now we have the following numbers in decimal form:

0.718

,

0.6875

,

0.7143

,

0.71

0.718,0.6875,0.7143,0.71

Next, we will arrange these decimals from smallest to largest:

\begin{itemize}

\item 0.6875 (which is \(\frac{11}{16}\))

\item 0.71

\item 0.7143 (which is \(\frac{5}{7}\))

\item 0.718 (which is 71.8%)

\end{itemize}

So, in order of size, starting with the smallest number:

11

16

,

0.71

,

5

7

,

71.8

%

16

11

,0.71,

7

5

,71.8%