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Let's look at our hundredths place. It is a 9. If we look to the next place value, the thousandths, we have a 7. If the next digit is 5-9, we round up. As it is 7, we round 9 up to 10. As this would switch the 9 to a 0, we add 1 to our 5 in the tens.
This leaves us with [tex] \boxed {3.6} [/tex].
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3.597
Look at the hundredths place. In this number, the 9 is in the hundredths place, so look to the right of 9.
Determine if the number is 5 or more, or 4 or less. If the number is 5+ then round the number in the hundredths place up, if the number is 4- then keep the number in the hundredths place the same.
7 is the number to the right of 9 - it is 5+ so you will round 9 up. It will round to 10, so that means the number on the LEFT of 9 will get rounded up and everything after that becomes a 0.
3.597 becomes 3.60 (nearest hundredth).