Decimal division patterns over increasing place values

Learning Objectives Identify the pattern that emerges when a number is divided by increasing powers of 10. Predict the quotient of a number divided by 10, 100, 1000, etc., without performing long division. Articulate the relationship between the number of zeros in the divisor and the movement of the decimal point in the dividend. Represent decimal division problems as rational expressions of the form c / 10^n. Correctly place leading zeros as placeholders when dividing small numbers by large powers of 10. Apply these division patterns to evaluate simple rational functions for inputs that are powers of 10. If a pizza is shared among 10 friends, you get a slice. What happens to your slice if it's shared among 100, or 1,000 friends? 🍕 In this tutorial, we will explore th...

TermDefinitionExample Place ValueThe value of a digit based on its position in a number. In the decimal system, each place to the left of the decimal is 10 times larger than the one to its right.In 452.3, the '5' is in the tens place, representing 50. The '3' is in the tenths place, representing 3/10. Power of 10A number that can be written as 10 raised to an integer exponent (n). It's a 1 followed by 'n' zeros.100 is a power of 10 because it can be written as 10^2. 1000 is 10^3. DividendThe number that is being divided.In the expression 75 ÷ 10, the dividend is 75. DivisorThe number by which another number is divided.In the expression 75 ÷ 10, the divisor is 10. QuotientThe result of a division operation.In the expression 75 ÷ 10 = 7.5, the quotient is...

Division by Powers of 10 c \div 10^n To divide a number 'c' by a power of 10 (10^n), move the decimal point in 'c' to the left by 'n' places. The value of 'n' is equal to the number of zeros in the divisor. Rational Expression Form c \div x = \frac{c}{x} Any division problem can be written as a rational expression (a fraction). This is useful for connecting arithmetic patterns to algebraic functions. Placeholder Zeros If c < 10^n, then \frac{c}{10^n} < 1 When moving the decimal point to the left, if you run out of digits, add leading zeros between the decimal point and the first non-zero digit as placeholders.