Math 1012 - Unit 3 (Decimals & Percents)

Math 1012 - Unit 3

DECIMALS & PERCENTAGES

Multiple Choice

Write 2.364 in word form.

• two and three hundred sixty -four thousandths

• two and three hundred sixty-four tenths

Writing Decimals as Simplified Fractions

• Every decimal can be written as a fraction.

• To convert a decimal to a fraction, place the number after the decimal point in the numerator of the fraction and place the number 10, 100, or 1,000, or another power of 10 in the

  denominator.

• For example, 0.5 would be written as 5/10

Multiple Choice

Write 0.25 as a fraction.

• 1/4

• 1/2

Comparing Decimals

Strategies for Comparing Decimals

• Use a number line to assist with comparing decimals, as you did with whole numbers.

• Compare decimals beginning with their digits from left to right.

• When two digits are not equal, the one with the greater digit is the larger number.

Multiple Choice

Use < or > for [ ] to write a true sentence: 45.675 [ ] 45.649.

• <

• >

Adding Decimals

• To add decimals:

  Align the decimal points, which will allow all the digits to be aligned according to their place values.

• Add just as you would add whole numbers, beginning on the right and progressing to the left.

• Write the decimal point in the sum, aligned with the decimal points in the numbers being added.

Substacting Decimals

• To subtract decimals:

  Align the decimal points, which will allow all of the digits to be aligned according to their place values.

• Subtract just as you would subtract whole numbers, beginning on the right and progressing to the left.

• Align the decimal point in the difference directly below the decimal points in the numbers that were subtracted.

Multiple Choice

Helene ran the 100-meter dash twice on Saturday. The difference between her two times was 0.3 seconds. Which pair of numbers below could have been her individual race times?

• A) 14.22 and 14.25 seconds

• B) 14.22 and 17.22 seconds

• C) 14.22 and 14.58 seconds

• D) 14.22 and 13.92 seconds

Multiplying Decimals

Multiplying Decimals

• Multiplying decimals is the same as multiplying whole numbers except for the placement of the decimal point in the answer.

• When you multiply decimals, the decimal point is placed in the product so that the number of decimal places in the product is the sum of the decimal places in the factors.

Multiplying a Decimal by a Power of Ten

• To multiply a decimal number by a power of ten (such as 10, 100, 1,000, etc.), count the number of zeros in the power of ten. Then move the decimal point that number of places to the right.

• For example, 0.054 • 100 = 5.4. The multiplier 100 has two zeros, so you move the decimal point in 0.054 two places to the right—for a product of 5.4.

Multiple Choice

A button has a diameter of 20 millimeters. What is the area of the button? Use 3.14 as an approximation of π . (A=π r^2)

• 314 mm

• 1,256 mm

• 31.4 mm

Dividing Decimals

Dividing Decimals

• Dividing Decimals by Whole Numbers. Divide as you would with whole numbers. Then place the decimal point in the quotient directly above the decimal point in the dividend.

  
  

• Dividing by Decimals. To divide by a decimal, multiply the divisor by a power of ten to make the divisor a whole number. Then multiply the dividend by the same power of ten. You can think of this as moving the decimal point in the dividend the same number of places to the right as you move the decimal point in the divisor.

• Then place the decimal point in the quotient directly over the decimal point in the dividend. Finally, divide as you would with whole numbers.

Multiple Choice

Divide: 25.095 ÷ 0.5.

• 50.19

• 5.019

Converting Percents, Decimals, and Fractions

Percent

• A percent is a ratio of a number to 100. Per cent means “per 100,” or “how many out of 100.” You use the symbol % after a number to indicate percent.

• Ex. 12% = 12 percent = 12 parts out of 100 = 12/100

Multiple Choice

Write 0.645 as a percent and as a simplified fraction.

• 64.5% = 129/200

• 6.45% = 12/200

• 64.5% = 645/1000

Mixed Numbers

Multiple Choice

Write 4.12 as a percent and as a simplified fraction.

• 412% and 4 12/100

• 412% and 4 3/25

• 412% and 4 1/2

Solving Percent Problems

Multiple Choice

18 is what percent of 48?

• 37.5%

• 3.75%

• 27%