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# Xavier rounds the number \$x\$ to the nearest integer and gets \$8\$...

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Xavier rounds the number \$x\$ to the nearest integer and gets \$8\$. Meanwhile, Yolanda rounds the same number \$x\$ to the nearest tenth, then passes her answer to Zazeela, who rounds that answer to the nearest integer and gets \$9\$. Yet, believe it or not, they all rounded correctly! (a) Give a specific number \$x\$ for which this scenario could happen. Explain why it happens. (b) Find all numbers \$x\$ for which this scenario could happen.

Explain how you know you found them al and how you got the numebrs please and thank you.

Dec 13, 2019

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rounding to the nearest integer means anything from 7.5 to 8.49 will be rounded to 8

rounding to the nearest 10th means anything from 8.45 to 8.54 will be rounded to 8.5

Then according to the first rule above, rounding to the nearest integer will result in 9

So any number from 8.45 to 8.49 would cause this scenario...rounding to the nearest integer will result in '8'

if you FIRST round to the nearest 10th you will round to 8.5     then rounding to the nearest integer results in '9' ....

Dec 13, 2019

#1
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rounding to the nearest integer means anything from 7.5 to 8.49 will be rounded to 8

rounding to the nearest 10th means anything from 8.45 to 8.54 will be rounded to 8.5

Then according to the first rule above, rounding to the nearest integer will result in 9

So any number from 8.45 to 8.49 would cause this scenario...rounding to the nearest integer will result in '8'

if you FIRST round to the nearest 10th you will round to 8.5     then rounding to the nearest integer results in '9' ....

ElectricPavlov Dec 13, 2019