Question

Elena is organizing her craft supplies. She estimatesthat her jars will fit 1,000 buttons or 50 large beads.They actually fit 677 buttons or 22 large beads. DoesElena's estimate about the buttons or her estimateabout the large beads have less percent error? To thenearest percent, how much less?

Answer 1

Step 1

Given;

`\begin{gathered} Elena-\text{ estimates her jar will take 1000 buttons or 50 large beads} \\ Her\text{ Jar actually takes 677 buttons or 22 large beads} \end{gathered}`

Required; To find if Elena's estimates have percentage error, to which percent, and how much less

Step 2

State the formula for percentage error

`\text{ \% error=}(|Approximate-exact|)/(exact)*100`
`Elena^(\prime)s\text{ estimate about the button has a percentage error }`
`\begin{gathered} For\text{ buttons} \\ Approximate=1000 \\ Exact=677 \end{gathered}`
`\text{ \%error=}(|1000-677|)/(677)*100=47.71048744\text{\%}`

`\text{ \% error=}(28)/(22)*100=127.272727...\text{\%}`

Percent errors tells you how big your errors are when you measure something in an experiment. Smaller values mean that you are close to the accepted or real value. For example, a 1% error means that you got very close to the accepted value, while 45% means that you were quite a long way off from the true value.

The percentage error for buttons with about 47.71% is less than that of the large beads which is about 127.273%.

How much less of the percentage error to the nearest percent will be;

`\begin{gathered} =79.56223986 \\ \approx80\text{\%} \end{gathered}`