6.2 Operations on Decimals

Addition and Subtraction

Could use base 10 manipulatives – unit as hundredths block; tenth as flat; hundredth as long, etc.

“convert to problem we already know”

Rename as fractional equivalent and get common denominator.

Relate to using place values.

7.812 + 14.07 + 17

54.03 - 7.154

Traditional Algorithm - "line up the decimal points"

#8 Continue the pattern (arithmetic or geometric)

b) 0.3, 0.5, 0.7, 0.9, 1.1, ___, ___, ___

d) 0.2, 1.5, 2.3, 4.1, 5.4, ___,___,___

Multiply Decimals

Convert to fractions - Watch the denominators when express as powers of 10

4.01 ´ 6.2

0.04 ´ 0.003

Traditional Algorithm - multiply like "whole numbers" and count total number of decimal places.

Note: In denominator

Scientific Notation

In scientific notation, a positive number is written as the product of

1) a number greater than or equal to 1 and less than 10

and 2) an integer power of 10. 

Change to scientific Notation

4,810                           0.00052                     97.6                   1,000,000

Change to standard form

Express quotient in scientific notation  

Divide Decimals

For division by a whole number, change decimals to fractions.

.96 ¸ 3

If divisor is a decimal, express the division as a fraction and multiply by appropriate power of ten to express as division by whole number. This translates to the traditional algorithm of “moving the decimal point of the divisor all the way to the right, and move the dividend the same number of places”

0.45 ¸ 0.03

13.169 ¸ 0.013

** If n is divided by a number less than one, then n increases in size **

#7 Flo-Jo set a world record for women’s 100-m dash in the 1988 Summer Olympics. She covered the distance in 10.49 sec. If 1 m is equivalent to 39.37 in., express Griffith-Joyner’s speed in terms of miles per hour.

Mental Computation pg 382

1. Breaking and bridging 2.5 + 1.7 + 4.48

2. Using compatible numbers 6.81 + 2.75 + 3.19 + 1.15

3. Making compatible numbers 4.36 + 2.59

4. Balancing with decimals in subtraction 3.62 – 1.35

5. Balancing with decimals in division.

Mentally compute the number to fill in the blank.

Rounding Decimals

Round 8.3546

a) to the nearest tenth, b) to the nearest thousandth

c) to the nearest whole number d) to the nearest thousandth

Estimating Decimal Computations using rounding – page 383

Money – especially quarters

#20 Audrey wants to buy some camera equipment to take pictures. To estimate the total cost, she rounds each price to the nearest dollar and add the rounded prices. What is her estimate for the items listed?

Camera $54.56; Film $4.50; Case $17.85