Lesson 1: Round a given decimal to any place using place value understanding and the vertical number line.

Property

To find the rounding bounds for a number, first decompose it based on the target place value. When rounding to a particular place value, determine how many units of that place value the number contains. This value gives you the lower bound, and the next consecutive value is the upper bound.

Examples

• To round $153$ to the nearest ten, we see that $153$ has $15$ tens ($15 \times 10 = 150$). The lower bound is $15$ tens ($150$) and the upper bound is $16$ tens ($160$).

• To round $4.37$ to the nearest tenth, we see that $4.37$ has $43$ tenths ($43 \times 0.1 = 4.3$). The lower bound is $43$ tenths ($4.3$) and the upper bound is $44$ tenths ($4.4$).

Property

When rounding a number to a place value greater than its largest place value, the number lies between 0 and 1 unit of that target place value. The lower bound for rounding is always 0.

Examples

• To round $87$ to the nearest hundred: $87$ has 0 hundreds, so it is between 0 hundreds ($0$) and 1 hundred ($100$).

• To round $0.73$ to the nearest one: $0.73$ has 0 ones, so it is between 0 ones ($0$) and 1 one ($1$).

Property

To round a number on a number line, first find the closest smaller number (the lower number) and the closest bigger number (the upper number) for the place you are rounding to. Then find the middle point between them.

• If the number is smaller than the middle, round down to the lower number.
• If the number is equal to or bigger than the middle, round up to the higher number.

Examples

Property

The result of rounding a number depends on the place value to which you are rounding. A single number can have multiple rounded values, each corresponding to a different place value and level of precision.

Examples