Metric Conversion and Multiplication by Powers of 10

10 min

Narrative

In this Number Talk, students find products of a decimal number and a power of 10 and quotients of a whole number and a power of 10, the value of which is a decimal. This skill will be useful throughout the next several lessons as students convert between different metric units of measure and also specifically address how a whole or decimal number changes when it is multiplied or divided by a power of 10.

Launch

  • Display the first expression.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time
Teacher Instructions
  • Record students’ answers and strategies.
  • Keep the expressions and the work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 100×1.5100 \times 1.5
  • 1,000×1.51,000 \times 1.5
  • 15÷1015 \div 10
  • 15÷10015 \div 100

Sample Response

  • 150: It’s 100 and half of another 100.
  • 1,500: It’s 1,000 and half of 1,000.
  • 1.5: I pictured it as a fraction, 1510\frac {15}{10}, which is equal to 1 and 5 tenths.
  • 0.15: 15÷100=15×110015 \div 100 = 15 \times \frac{1}{100} and that is equal to 0.15.
Activity Synthesis (Teacher Notes)
  • “What is the same about the values of the expressions?” (There is a 1 and a 5 in each value.)
  • “What is different about the values of the expressions?”(Some of them are whole numbers and some are decimals.)
Standards
Addressing
  • 5.NBT.2·Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
  • 5.NBT.A.2·Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

20 min

15 min