Question

How do you round 0.4062 to the nearest hundredth?

Answer 1

`0.4color(blue)(1)`

Explanation:

Round " to the nearest hundredth" is the same as saying
"round to two decimal places"

This means that we only want 2 decimals in the number instead of all 4.

When we round off a number, we need to look at the value of the digit *AFTER* the rounding we need.

Rounding to 3 decimal places, look at the digit in the 4th place.
Rounding to 2 decimal places , look at the digit in the 3rd place .
Rounding to 1 decimal place, look at the digit in the 2nd place.

Rounding to the nearest hundred, look at the digit in the tens place.

In `0.4color(blue)(0)color(red)(6)2`

The digit `color(blue)(0)` is in the 2nd decimal place (hundredths)
When we round off, it can either stay as `color(blue)(0)` or round up to `color(blue)(1).`
It depends on the digit which follows.

The next digit is `color(red)(6)`

If this next digit is 5 or more (5, 6 ,7,8,9), the digit before it rounds UP .
If this next digit is 4 or less (0,1,2,3,4), the digit before it stays the SAME.

So the number `0.4color(blue)(0)color(red)(6)2` rounds up to `0.4color(blue)(1)`

Note the following.
We only write 2 decimal places.
The `2` at the end has no effect on the rounding at all.
The size of the number is the same, it is just not as accurate.

Answer 2

See explanation

Explanation:

`0.4062`

Write as `4/10+0/100+6/1000+2/10000`

`color(red)(color(white)("ddddddddddd")color(white)(2/2)uarr)`
`color(red)(color(white)("ddddddddd") " hundredths")`

The number to the right of the 100th place is 6 which is bigger than or equal to 5 so we round up.

This means that instead of `0.4062` we have `0.41`
The 0 has increased by 1.

All the digits to the right of the red arrow are discarded leaving just `0.41`