Section 7.2 Computations with Decimals MTH 232 Section 7.2 Computations with Decimals

Objectives Be able to round a decimal number to an indicated value. Be able to add and subtract decimals. Be able to order decimals. Be able to multiply decimals. Be able to divide decimals.

Rounding Decimals The algorithm for rounding decimals is the same as rounding whole numbers (refer to Section 3.4 if you need a refresher), with one notable exception: you do not add zeroes after the rounded digit. For example, 364 rounded to the nearest ten is 360, but 36.47 rounded to the nearest tenth is 36.5.

Adding and Subtracting Decimals Adding and subtracting decimal numbers can be modeled in a manner similar to adding and subtracting whole numbers by using base-ten blocks or ten-dollar bills, dollar-bills, dimes and pennies. Algorithmically we write the problem in vertical style, lining up the decimal points. Be sure to reinforce and use estimation and mental calculation as well.

Examples:

Ordering Decimal Numbers First, compare the integer parts of the two numbers (the part to the left of the decimal point), if any. If the integer parts are the same, or if there are no integers parts, start at the tenths place and compare digits. Moving to the right, keep comparing until one digit is greater than the other.

Examples:

Multiplying Decimals To multiply two decimals, do the following: Multiply as with integers. Count the total number of digits to the right of the decimal points of each number. Call that number t. Starting at the right of your product, move the decimal point t places to the right. Again, use estimate and mental calculation.

An Example:

Dividing Decimals Move the decimal point in the divisor until the number becomes an integer (no digits to the right of the decimal). Move the decimal point in the dividend the same number of places. Divide as with whole numbers. Again, use estimation and mental computation.

Example: