Multiplying and Dividing Numbers by Powers of 10
Multiplying and Dividing Numbers by Powers of 10 is a Grade 5 math skill from Eureka Math that reinforces how multiplying or dividing any number by a power of 10 shifts its digits left or right. Students apply this consistently to whole numbers and decimals, building fluency and a systematic understanding of the base-10 number system. This skill supports all decimal operations and number sense in 5th grade.
Key Concepts
Property To multiply by a power of 10, move the decimal point to the right. $$a \times 10^n$$ To divide by a power of 10, move the decimal point to the left. $$a \div 10^n$$.
Examples $4.53 \times 10^3 = 4.53 \times 1,000 = 4,530$ $67 \div 10^2 = 67 \div 100 = 0.67$ $18.9 \div 10^3 = 18.9 \div 1,000 = 0.0189$.
Explanation When multiplying a number by a power of 10, such as $10^n$, you move the decimal point $n$ places to the right. When dividing a number by a power of 10, you move the decimal point $n$ places to the left. The exponent tells you exactly how many places to shift the decimal. You may need to add placeholder zeros if there are not enough digits.
Common Questions
What happens to a number when you multiply by 10 in Grade 5?
Every digit shifts one place to the left, making the number 10 times greater. For example, 4.7 x 10 = 47 and 230 x 10 = 2,300.
What happens when you divide a decimal by 100?
Every digit shifts two places to the right, making the number 100 times smaller. For example, 56 ÷ 100 = 0.56.
Why is multiplying and dividing by powers of 10 an important Grade 5 skill?
It is the foundation for all decimal arithmetic, scientific notation, metric unit conversions, and understanding of the place value structure of the number system.
What Eureka Math Grade 5 chapter covers multiplying and dividing by powers of 10?
Eureka Math Grade 5 covers this skill in its place value and decimal chapters as a foundational concept that underpins all decimal operations.
How do you multiply 0.04 by 1,000?
Multiplying by 1,000 shifts digits three places to the left. 0.04 x 1,000 = 40. The digit 4 moves from the hundredths place to the tens place.