Decimals- rounding

Links and useful resources

• gr7's Prealgebra Course Outline START HERE<<<
• AoPS Online Textbook
• IXL Grade 7 index
• IXL Grade 8 index
• AoPS Alcumus
• IXL prealgebra practice index
• OpenSTAX Prealgebra-1 textbook

Concept summary and lesson

• rounding decimals
• rounding negative numbers

The main idea of rounding is this: Pick the rounded digit that is closest to the true value. That means that you'll always either keep it the same, or increase the digit by one. That's true even if the number is negative!

Here's how you do it:

1. Keep all of the digits in places that your answer needs (so if you are rounding to thousandths, keep all the digits up and including the thousandths place)
2. Look at the first digit of what's left over. If it's equal or greater than 5, you need to increase the last digit in your rounded number by one. Don't "add" - you're literally just increasing the digit value! This matters for negative numbers, because if you "add a thousandth" you'll end up decreasing the digit value!
3. If the digit you increased was a 10, act like you're doing addition with a positive number and carry it appropriately.

Think of negatives this way: is -1.9 closer to -2 or -1? Well, the difference from -2 is 0.1, and the difference from 1 is 0.9, so pretty clearly it's closer to -2. But, you might say, that made the number less than it started! This is true in one sense, in that it made it more negative. But, the digit value still either stays the same or increases by one. Whether that makes the number more negative or more positive depends on the sign of the number, but it doesn't change what we do when we're rounding.

Examples

• Round ($-1.995$) to the nearest hundredth
  • First, keep $-1.99$, and look at the first digit we're discarding: $5$.
  • It's greater than or equal to $5$, so we're going to increase our rounded digit by one. $-1.9[9+1]$
  • The digit was a 9, which means we have to carry the addition until it stops overlowing:
    • $(-1.[9+1]0)$
    • $-2.00$
  • Rounding made the number more negative, because it was closer to $-2.00$ than to $-1.98$
• Round ($-1.994$) to the nearest hundredth
  • First, keep ($-1.99$) and look at the first discarded digit: $4$
  • It's less than $5$, so we don't need to change anything and our answer is ($-1.99$)

Media resources

• Youtube search for "rounding decimals"
• Youtube search for "rounding negative numbers"

Guided practice

• round -8.4995 to the nearest integer, tenth, and thousandth.

Homework

• #hw (math) (gr7) 6.2 Rounding (p. 258) 2025-01-24