# How do you round 105 to the nearest hundred?

Oct 22, 2016

100

#### Explanation:

Showing what I call the cut off point (in red)

In your mind only write the number as:

$1 \text{ "color(red)(|)" "0" } 5$
$\text{ } \textcolor{w h i t e}{.} \textcolor{red}{\uparrow}$
$\textcolor{red}{\text{cut off point}}$

The digit to the right of the cut off point is less than 5 so we round down. That is, change all the digits to the right of the cut off point as 0 so:

105 is 100 to the nearest one hundred.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Foot note}}$

If the digit to the right of the cut off point had been 5 or more then we would have 200 to the nearest one hundred

6 satisfies the condition of 5 or more so the digit to the LEFT of the cut of point has 1 added to it.

Consider to the nearest 10

$12 \to \text{nearest 10 } = 10$ Rounding down
$13 \to \text{nearest 10 } = 10$ Rounding down
$14 \to \text{nearest 10 } = 10$ Rounding down

$15 \to \text{nearest 10 } = 20$ Rounding up
$16 \to \text{nearest 10 } = 20$ Rounding up
$17 \to \text{nearest 10 } = 20$ Rounding up
$18 \to \text{nearest 10 } = 20$ Rounding up
$19 \to \text{nearest 10 } = 20$ Rounding up
$20 \to \text{nearest 10 } = 20$ No rounding
$21 \to \text{nearest 10 } = 20$ Rounding down
$22 \to \text{nearest 10 } = 20$ Rounding down
$23 \to \text{nearest 10 } = 20$ Rounding down
$24 \to \text{nearest 10 } = 20$ Rounding down

$25 \to \text{nearest 10 } = 30$