This version of the chart helps you read the number. Begin all the way to the left and read, “Two hundred thirty-four quintillion, eight hundred forty-five quadrillion, twenty-one trillion, three hundred forty-nine billion, two hundred thirty million, four hundred sixty-seven thousand, three hundred four.”
Close Enough for Rock ‘n’ Roll: Rounding and Estimating
As numbers get longer, calculations become tedious, and you’re more likely to make a mistake or just give up. When you’re working with long numbers, simplifying your work by rounding numbers and estimating values is sometimes helpful.
When you round a number, you change some of its digits to placeholding zeros. And when you estimate a value, you work with rounded numbers to find an approximate answer to a problem. In this section, you build both skills.
Rounding numbers
Rounding numbers makes long numbers easier to work with. In this section, I show you how to round numbers to the nearest ten, hundred, thousand, and beyond.
Rounding numbers to the nearest ten
The simplest kind of rounding you can do is with two-digit numbers. When you round a two-digit number to the nearest ten, you simply bring it up or down to the nearest number that ends in 0. For example:
Even though numbers ending in 5 are in the middle, always round them up to the next-highest number that ends in 0:
Numbers in the upper 90s get rounded up to 100:
When you know how to round a two-digit number, you can round just about any number. For example, to round most longer numbers to the nearest ten, just focus on the ones and tens digits:
Occasionally, a small change to the ones and tens digits affects the other digits. (This situation is a lot like when the odometer in your car rolls a bunch of 9s over to 0s.) For example:
Rounding numbers to the nearest hundred and beyond
To round numbers to the nearest hundred, thousand, or beyond, focus only on two digits: the digit in the place you’re rounding to and the digit to its immediate right. Change all other digits to the right of these two digits to 0s. For example, suppose you want to round 642 to the nearest hundred. Focus on the hundreds digit (6) and the digit to its immediate right (4):
I’ve underlined these two digits. Now just round these two digits as if you were rounding to the nearest ten, and change the digit to the right of them to a 0:
Here are a few more examples of rounding numbers to the nearest hundred:
When rounding numbers to the nearest thousand, underline the thousands digit and the digit to its immediate right. Round the number by focusing only on the two underlined digits and, when you’re done, change all digits to the right of these to 0s:
Even when rounding to the nearest million, the same rules apply:
1
(a) 83
(b) 217
(c) 1,885
(d) 6,496
2 Round the following numbers to the nearest hundred:
(a) 347
(b) 2,251
(c) 7,950
(d) 39,974
3 Round the following numbers to the nearest thousand:
(a) 6,543
(b) 9,287
(c) 22,501
(d) 799,643
4 Round the following numbers to the nearest million:
(a) 5,454,545
(b) 10,730,421
(c) 98,765,432
(d) 5,555,555,555
Estimating value to make problems easier
When you know how to round numbers, you can use this skill in estimating values. Estimating saves you time by allowing you to avoid complicated computations and still get an approximate answer to a problem.
