Multiplying Decimals
? Video Tutorial Step 1: Ignore decimal points initially and multiply the numbers as whole numbers. For example, multiply 0.34 × 2.5 as 34 × 25 = 850. Step 2: Add up the decimal places in both original numbers. For 0.34 (2 places) and 2.5 (1 place), the total is 3 decimal places. Step 3: […]
Rational Numbers and their location on a Number Line
? Video Tutorial Definition of Rational Numbers: Rational numbers are numbers that can be written as a fraction of two integers (a/b) where b ? 0. Examples of Rational Numbers: Fractions like 2/3, integers like -2, terminating decimals like 0.7, and recurring decimals like 0.3 recurring (1/3) are all rational numbers. Irrational Numbers: Irrational numbers […]
Movement of the Decimal Point
? Video Tutorial Multiplying by Powers of 10: When multiplying by 10, 100, or 1000, move the decimal point 1, 2, or 3 places to the right, respectively. Fill empty spaces with zeros if needed. Dividing by Powers of 10: When dividing by 10, 100, or 1000, move the decimal point 1, 2, or 3 […]
Convert Recurring Decimals to Fractions
? Video Tutorial Converting Recurring Decimals to Fractions: Start by setting the recurring decimal as ‘$x$’, then use multiplication to align the repeating parts, making subtraction possible to eliminate them. One-Digit Recurring Example: Let $x = 0.333ldots$; multiply by 10 to get $10x = 3.333ldots$ Subtract the equations to find $9x = 3$. So $x […]
Laws of Indices (Same Base, Same Indices)
? Video Tutorial Laws for Same Base: For multiplication, add the indices (e.g., $2^3 times 2^4 = 2^7$). For division, subtract the indices (e.g., $4^5 div 4^3 = 4^2$). Laws for Same Index: For multiplication, multiply the bases and keep the index (e.g., $2^3 times 5^3 = 10^3$). For division, divide the bases and keep […]
Negative Indices and Power of a Power
? Video Tutorial Negative Indices Rule: A negative index means taking the reciprocal of the base with a positive index. For example: $2^{-3} = frac{1}{2^3} = frac{1}{8}$ Applying Negative Indices on Fractions: Flip the fraction and use the positive index. For example: $left(frac{2}{3}right)^{-2} = left(frac{3}{2}right)^2 = frac{9}{4}$ Power of a Power Rule: When raising a […]
Decimals and Fractions
? Video Tutorial Decimals and Everyday Use: Decimals, commonly used for prices and measurements, consist of a whole number and a fractional part separated by a decimal point. Converting Decimals to Fractions: To convert a decimal to a fraction, count decimal places for the denominator (e.g., 0.4 becomes 4/10, 0.75 becomes to 75/100), then simplify […]
Comparing and Rounding Decimals
? Video Tutorial Decimal Places: Decimal places represent tenths, hundredths, and thousandths, making it easy to express parts of a whole in precise terms. Rounding Decimals Rules: To round, check the digit to the right of your desired place. Round down if it’s less than 5; round up if it’s 5 or more. Rounding Examples: […]
Fractions to Decimals Using Long Division
? Video Tutorial Converting Fractions to Decimals: Rewrite the fraction (e.g., 21/16) as a division problem (e.g., 21 ÷ 16) and perform long division. Terminating vs. Recurring Decimals: A terminating decimal has a finite number of digits, while a recurring decimal has digits that repeat indefinitely. Identifying Recurring Decimals: During long division, if remainders start […]
Prime Numbers and Prime Factorization
? Video Tutorial Definition of Prime Numbers: Prime numbers have exactly two factors (1 and the number itself). 1 is not a prime number, and 2 is the smallest prime number. Common Prime Numbers under 20: 2, 3, 5, 7, 11, 13, 17, 19 Prime Factorisation: Expresses any number as a product of prime numbers. […]