Chapter 2- Decimals

What will be covered? Place Value Chart Comparing Decimals Rounding Decimals Add and Subtract Decimals Multiply and Divide Decimals Order of Operations with Decimals Fraction to Decimal

Place Value Chart

Comparing Decimals Line up the decimals vertically. Start at the left and compare corresponding digits. If the digits are the same, move one place to the right. When two digits are different, the larger number is the one with the larger value.

Example: Comparing Decimals List from Smallest to Largest 1.834, 1.83, 1.381, 1.38, 1.8 Answer: 1.38, 1.381, 1.8, 1.83, 1.834 1.834 1.83 1.381 1.38 1.8 00

Example 2: Compare Decimals List from smallest to largest 15.002, 15.02, 15.001, 15.018, 15.0019 Answer: 15.002 15.02 15.001 15.018 15.0019 15.001, 15.0019, 15.002, 15.018, 15.02 0 0

Rounding Decimals Circle the digit value to round to, and draw an arrow to the number to the right If the value is 5 or greater, round the digit value up one If the value is less than 5, drop the values to right of digit

Example: Rounding Decimal Round 137.8945 to the nearest hundredths 1 3 7.8 9 4 5 5 or Greater? No Then drop values 137.89 Round 0.3899 to the nearest thousandth 0.39 0.3 8 9 9

Examples: More on rounding Round to the nearest whole number. This is the same thing as rounding to the nearest ones place. 8. 7 6 5 9.0 or 9 4 9 5.2 4 5 495.00 or 495

Adding and Subtracting Decimals Write the numbers to be added vertically and line up the decimal points. Extra zeros may be placed to the right of the decimal points if needed. Add or subtract all the digits with the same place value, starting with the right column and moving to the left. Place the decimal point of the sum or difference in line with the decimal points of the numbers added.

Examples on Adding Decimals 3.1 + 2.16 = 3.1 2.16 + 5.26

Example: Adding Decimals Step 1 Step 2 Step 3 15.3000 +1.1109 15.3000 +1.1109 16.4109 15.3 +1.1109

Example: Subtracting Decimals Step 1 Step 2 Step 3 15.87 - 1.649 15.870 - 1.649 15.870 1.649 14.221

Multiplying Decimals Steps Set up in multiplying form – don’t worry about lining up decimals or trailing zeros Multiply Count decimals places in both multiplied numbers Move decimal point in final answer

Example: Multiplying Decimals Multiply 21.7 x .23 Step 3 Step 1 Step 2 3 Decimal Places 4.991 21.7 X .23 21.7 X .23 651 +4340 4991

More Examples on Multiplication Step 1 Step 2 Step 3 5.261 45 26305 210440 236745 5.261 45 236. 745 x x +

Dividing a Decimal by a Whole Number Set up the division problem Place the decimal point for the quotient directly above the decimal point in the dividend. Then, divide if the numbers were whole numbers. Validate by multiplication.

Dividing by a Whole Number The decimal points are aligned, one above the other. 2.16 . 16 12 8 48 Divide as you normally divide whole numbers.

Dividing by a Decimal When dividing a decimal by another decimal, the division problem is converted into an equivalent problem that has a whole number as a divisor. Dividing by a Decimal Make the divisor a whole number by moving the decimal point to the right. Mark that position with a caret (). Count the number of places the decimal point moved. Move the decimal point in the dividend to the right the same number of places. Mark that position with a caret. Place the decimal point of your answer directly above the caret marking the point of the dividend. Divide as with whole numbers.

Dividing by a Decimal 2.3 366 549 Example: Divide 4.209 ÷ 1.83. . . . Move each decimal point to the right two places. . . Place the decimal point of the answer directly above the caret. 2.3 .  Mark the new position by a caret (). 366 549 Divide as normal.

Dividing by a Whole Number Example: Divide 263.82 ÷ 7 and round to the nearest hundredths. 37.688 Carry out the division to the thousandths place, and then round. An extra zero was added to carry out the division to the required place. 21 53 49 48 42 62 56 60 37.688 is rounded to 37.69 (the nearest hundredths). Note that the remainder is not zero.

Order of Operations 0.3 x 0.5 + ( 0.4x 0.4x 0.4) – 0.036 .15 + 0.064 – 0.036 0.150 + 0.064 0.150 + 0.064 0.214 -0.036 Validate 0.036 0.178 0.214 0.178 0.214

Fraction to Decimal

Fraction to Decimal Validation: