Finding a Decimal Between Two Decimals
Finding a Decimal Between Two Decimals is a Grade 5 math skill from Illustrative Mathematics Chapter 5 (Place Value Patterns and Decimal Operations) that teaches students to find a number between two consecutive decimals by adding a trailing zero to both numbers, extending to the next decimal place. This reveals infinitely many numbers between any two decimals and reinforces the concept of equivalent decimals.
Key Concepts
To find a number $x$ between two decimals $a$ and $b$ (where $a < b$), rewrite both as equivalent decimals with an additional place value by adding a trailing zero. This allows you to identify a value for $x$ such that $a < x < b$.
Common Questions
How do you find a decimal between two decimals?
Add a trailing zero to both decimals to extend them to the next place value. This reveals numbers between them. For example, between 0.7 and 0.8: rewrite as 0.70 and 0.80, then any value from 0.71 to 0.79 works, such as 0.75.
Are there always numbers between two decimals?
Yes, there are infinitely many decimals between any two decimals, no matter how close they are. By adding trailing zeros, you can always find a smaller place value with numbers in between.
What chapter covers finding a decimal between two decimals in Illustrative Mathematics Grade 5?
Finding a decimal between two decimals is covered in Chapter 5 of Illustrative Mathematics Grade 5, titled Place Value Patterns and Decimal Operations.
What is an example of finding a decimal between two decimals?
Find a number between 5.01 and 5.02: rewrite as 5.010 and 5.020. Any thousandths value between them works, such as 5.015. Between 0.7 and 0.8: rewrite as 0.70 and 0.80, answer could be 0.73.
What does adding a trailing zero do to a decimal?
Adding a trailing zero creates an equivalent decimal at a more precise place value without changing the value. 0.7 and 0.70 are equal, but expressing both numbers at the hundredths place reveals room for values like 0.75 between them.