MATH 0925 MODULE 6 EXAM STUDY PACK TOPICS COVERED: * Decimals * Place Value * Expanded Form * Word Form * Standard Form * Rounding * Decimals to Fractions * Fractions to Decimals * Comparing and Ordering Decimals * Perfect Squares * Square Roots * Rational and Irrational Numbers * Adding Decimals * Subtracting Decimals * Multiplying Decimals * Dividing Decimals * Mean * Median * Mode * Range FLASHCARDS Q: What is the tenths place ? A: The first digit to the right of the decimal. Q: What is the hundredths place? A: The second digit to the right of the decimal. Q: What is the thousandths place? A: The third digit to the right of the decimal. Q: Write 0.352 in expanded form. A: 3(0.1) + 5(0.01) + 2(0.001) Q: Write 4.2706 in expanded form. A: 4 + 2(0.1) + 7(0.01) + 6(0.0001) Q: How do you write a decimal in word form? A: Read the whole number, say “and,” then read the decimal part and its place value. Q: Write 24.9 in word form. A: Twenty-four and nine tenths. Q: How do you round decimals? A: Look at the digit to the right of the rounding place. Q: What happens when the next digit is 5 or more? A: Round up. Q: What happens when the next digit is less than 5? A: Keep the digit the same. Q: Convert 0.46 to a fraction. A: 46/100 = 23/50. Q: Convert 0.12 to a fraction. A: 12/100 = 3/25. Q: Convert 0.105 to a fraction. A: 105/1000 = 21/200. Q: How do you convert a fraction to a decimal? A: Divide numerator by denominator. Q: How do you compare decimals? A: Compare digits from left to right. Q: Which is greater, 0.20 or 0.12? A: 0.20. Q: Which is greater, -8 or -9? A: -8. Q: What is 1²? A: 1. Q: What is 2²? A: 4. Q: What is 3²? A: 9. Q: What is 4²? A: 16. Q: What is 5²? A: 25. Q: What is 6²? A: 36. Q: What is 7²? A: 49. Q: What is 8²? A: 64. Q: What is 9²? A: 81. Q: What is 10²? A: 100. Q: What is 11²? A: 121. Q: What is 12²? A: 144. Q: What is √36? A: 6. Q: What is √49? A: 7. Q: What is √81? A: 9. Q: What is √121? A: 11. Q: What is √(16/49)? A: 4/7. Q: Is √(-100) a real number? A: No. It is not a real number. Q: What is a rational number? A: A decimal that stops or repeats. Q: What is an irrational number? A: A decimal that never stops and never repeats. Q: Is π rational or irrational? A: Irrational. Q: Is √2 rational or irrational? A: Irrational. Q: What is the rule for adding decimals? A: Line up decimal points. Q: What is the rule for subtracting decimals? A: Line up decimal points. Q: What is the rule for multiplying decimals? A: Multiply normally and count decimal places. Q: What is the rule for dividing decimals? A: Make the divisor a whole number. Q: What is the mean? A: Average. Q: How do you find the mean? A: Add all values and divide by the number of values. Q: What is the median? A: The middle value after ordering the data. Q: What is the mode? A: The value that appears most often. Q: What is the range? A: Largest value minus smallest value. IMPORTANT EXAM RULES 1. Line up decimals when adding and subtracting. 2. Count decimal places when multiplying. 3. Make the divisor a whole number before dividing. 4. Memorize perfect squares from 1² through 12². 5. Rational numbers stop or repeat. 6. Irrational numbers never stop and never repeat. 7. Mean = Average. 8. Median = Middle. 9. Mode = Most Common. 10. Range = Largest − Smallest. COMMON MISTAKES * Forgetting to line up decimals. * Forgetting to simplify fractions. * Mixing up mean and median. * Forgetting to count decimal places in multiplication. * Forgetting to move BOTH decimals in division. * Thinking all square roots are rational. * Forgetting that negative numbers closer to zero are larger. PRACTICE QUESTIONS 1. Round 45.0193 to the nearest hundredth. Answer: 45.02 2. Convert 0.36 to a fraction. Answer: 9/25 3. Convert 3/8 to a decimal. Answer: 0.375 4. Which is larger: 0.205 or 0.25? Answer: 0.25 5. Find √64. Answer: 8 6. Is √5 rational or irrational? Answer: Irrational 7. Add: 14.563 + 6.29 Answer: 20.853 8. Subtract: 24 − 8.0731 Answer: 15.9269 9. Multiply: 4.8 × 0.13 Answer: 0.624 10. Find the mean of 10, 20, 30. Answer: 20

Decimal

A number that contains a decimal point, representing a fraction of a whole.

Place Value

The value of a digit based on its position within a number.

Expanded Form

A way to write a number by showing the value of each digit.

Word Form

Writing a number using words instead of digits.

Standard Form

The usual way of writing numbers using digits.

Rounding

Adjusting a number to a nearby value, typically to make it simpler.

Decimals to Fractions

The process of converting a decimal number into a fraction.

Fractions to Decimals

The process of converting a fraction into a decimal number.

Comparing Decimals

Determining which of two decimal numbers is greater or lesser.

Perfect Squares

Numbers that are the square of an integer.

Square Roots

A number that produces a specified quantity when multiplied by itself.

Rational Numbers

Numbers that can be expressed as a fraction of two integers.

Irrational Numbers

Numbers that cannot be expressed as a simple fraction; they have non-repeating, non-terminating decimal expansions.

Adding Decimals

Combining decimal numbers while maintaining their decimal alignment.

Subtracting Decimals

Taking one decimal number away from another, aligning the decimal points.

Multiplying Decimals

The process of multiplying decimal numbers, counting decimal places in the product.

Dividing Decimals

The process of dividing one decimal number by another, adjusting to make the divisor a whole number.

Mean

The average of a set of numbers, calculated by adding them all up and dividing by the quantity.

Median

The middle number in a sorted set of numbers.

Mode

The number that appears most frequently in a set.

Range

The difference between the largest and smallest numbers in a set.

What do you need to remember when adding and subtracting decimals?

Line up decimals.

What should you do when multiplying decimals?

Count decimal places.

How do you divide decimals?

Make the divisor a whole number.

How do you identify rational numbers?

They stop or repeat.

What is the primary characteristic of irrational numbers?

They never stop and never repeat.

What is the measure of central tendency calculated by adding numbers and dividing by quantity?

Mean.

How is the median determined?

It is the middle value in a data set.

What does mode refer to in statistics?

The most frequently occurring value.

How is range calculated?

Largest number minus the smallest number.

What common mistake involves forgetting to align numbers during operations?

Not lining up decimals.