Welcome to this deck on rounding, bounds, and error intervals. You'll learn how to round numbers accurately, find the range of possible original values after rounding, and express this range as an error interval.

First, let's look at rounding to a certain number of decimal places. To do this, you look at the digit to the right of the place you're rounding to. If it's 5 or more, you round up. If it's 4 or less, you keep the digit the same. For example, to round 7.86 to one decimal place, we look at the second decimal digit, which is 6. Since 6 is 5 or more, we round the 8 up to 9, giving 7.9.

Rounding to significant figures is similar, but we count the digits from the first non-zero digit. For example, in the number 0.0458, the first significant figure is 4. To round this to one significant figure, we look at the next digit, 5. Since it's 5 or more, we round the 4 up to 5, giving 0.05.