Multiplying and Dividing by Powers of 10
Multiplying and Dividing by Powers of 10 is a Grade 5 math skill from Eureka Math that teaches students to efficiently multiply and divide numbers by 10, 100, 1,000 and their decimal equivalents. Students apply place value reasoning to shift digits left for multiplication and right for division. This skill builds fluency and connects whole number operations to decimal number sense.
Key Concepts
To multiply a number by a power of 10 ($10, 100, 1000, \dots$), move the decimal point to the right by the same number of places as there are zeros in the power of 10. To divide a number by a power of 10, move the decimal point to the left by the same number of places as there are zeros.
Common Questions
What is the rule for multiplying and dividing by powers of 10?
Multiplying by a power of 10 shifts digits to the left (makes the number larger); dividing shifts digits to the right (makes the number smaller). The number of places equals the exponent.
How do you multiply 0.4 by 100?
Multiplying by 100 shifts the decimal two places to the right. 0.4 x 100 = 40. The digit 4 moves from the tenths place to the tens place.
How do you divide 35 by 1,000?
Dividing by 1,000 shifts digits three places to the right. 35 ÷ 1,000 = 0.035. The digits shift from tens/ones to hundredths/thousandths.
What Eureka Math Grade 5 chapter covers multiplying and dividing by powers of 10?
Eureka Math Grade 5 covers multiplying and dividing by powers of 10 in its place value and decimal chapters, building a foundation for all decimal operations.
Why is understanding powers of 10 important in Grade 5?
Powers of 10 underlie the entire base-10 number system. Fluency with multiplying and dividing by them is essential for decimal operations, measurement conversions, and scientific notation.