Rounding Decimal Fractions
Welcome to the world of rounding! Today we will learn how to make numbers simpler and easier to work with.
1. What Is Rounding?
Definition
Rounding means replacing a number with a nearby approximate value that is easier to use in calculations.
Why do we round?
- It makes numbers easier to work with
- It lets us quickly estimate a result
- It is used in measurements and everyday calculations
- It helps us check whether an answer is reasonable
Real-life example
Price of an item: 47.89 som
Rounded: ≈ 48 som
This makes it easier to see whether you have enough money!
Where the Rule Comes From
Let us round 3.4682 to hundredths.
- The number contains 3.46 in whole hundredths.
- The remainder 0.0082 is less than one hundredth (0.01). It is a fraction of a hundredth between 0 and 1: 0.82 of a hundredth.
- The nearest numbers with two digits after the decimal point are 3.46 and 3.47. There is only one question: which of them is closer? 0.82 of a hundredth is closer to a whole hundredth, so 3.4682 ≈ 3.47.
The rule "if the digit to the right is 5 or more, round up" is a short way to answer this same question by looking at just one digit. The remainder is half of the place unit or more exactly when the next digit is 5, 6, 7, 8 or 9. If the remainder is exactly one half, we round up by agreement.