# Round to the Nearest Thousandth

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Rounding numbers coverts large numbers and decimal numbers to simpler forms which are then useful to solve or express in a given question. Rounding to the tenth’s place is rounding of a decimal number to the nearest one decimal space. Rounding to the hundredth’s place is rounding a decimal number to the nearest two decimal spaces. Rounding to the thousandth’s place is rounding a decimal number to the nearest three decimal spaces and so on. This concept is commonly used in many word problem and different calculations.

Example 1: Round the following numbers to the nearest thousandth.
a)    12.456712.   b) 45.3214.

Solution: Given are the decimal numbers 12.456712 and 45.3214.

a)     The decimal number 12.456712 has 6 decimal spaces the number in the thousandth space is 6.
For rounding the thousandth space the number right to 6 needs to be considered. Since number 7 is greater than 5.

Rounding to the thousandth space gives the value 12.457.

b)    The decimal number 45.3214 has 4 decimal spaces the number in the thousandth space is 1.
For rounding the thousandth space the number right to 1 needs to be considered. Since number 4 is smaller than 5.

Rounding to the thousandth space gives the value 45.321.

Example 2: Round the decimal number 0.3678 to the nearest thousandth.

Solution: Given are the decimal numbers 0.3678.

The decimal number 0.3678 has 4 decimal spaces the number in the thousandth space is 7.

For rounding the thousandth space the number right to 7 needs to be considered. Since number 8 is greater than 5.

Rounding to the thousandth space gives the value 0.368.