How do I round 526,472 to the closest ten thousand?

1 Answer

#53,000#

Explanation:

Let's first identify what place we're looking at:

#overbrace5^("hundred thousand")color(white)(0)overbracecolor(red)(2)^(color(red)("ten thousand"))color(white)(0)overbrace6^("thousand")color(white)(0)overbrace4^("hundred")color(white)(0)overbrace7^("ten")overbrace2^("one")#

When we round to the nearest something, let's first look at what the possible answers could be. In this case, to round to the closest ten thousand, we could have an answer:

#52,000#

or, since we're already part way to the next ten thousand,

#53,000#

Are we closer to 52,000 or to 53,000? Are we more than halfway to the next ten thousand? To figure that out, we look at the next digit down (in this case, the thousand):

#overbrace5^("hundred thousand")color(white)(0)overbracecolor(red)(2)^(color(red)("ten thousand"))color(white)(0)overbracecolor(blue)(6)^(color(blue)("thousand"))color(white)(0)overbrace4^("hundred")color(white)(0)overbrace7^("ten")overbrace2^("one")#

If that blue number is 0, 1, 2, 3, or 4, we aren't halfway yet and so the red number stays put at its value. If that blue number is 5, 6, 7, 8, or 9, then we're more than halfway and therefore need to round up to the next value.

In our question, the blue number, the thousands, is a 6. That means we're more than halfway to the next ten thousand and so should round up that red value by 1. Our answer then is #53,000#