Comparing Decimals to the Thousandths
Comparing Decimals to the Thousandths is a Grade 5 math skill from Illustrative Mathematics Chapter 5 (Place Value Patterns and Decimal Operations) where students compare two decimals by aligning decimal points and comparing digits from left to right (largest to smallest place value). The first position where digits differ determines which decimal is greater, with trailing zeros added to make lengths equal when needed.
Key Concepts
Property To compare two decimals, start from the leftmost digit and compare the digits in each place value. The first place where the digits differ determines which number is greater. Use the symbols $ $ (greater than), $<$ (less than), or $=$ (equal to).
Examples To compare $0.528$ and $0.541$, we see the tenths are the same ($5$). Comparing the hundredths, we find that $2 < 4$, so $0.528 < 0.541$. To compare $0.7$ and $0.689$, we start with the tenths place. Since $7 6$, we know that $0.7 0.689$. To compare $3.45$ and $3.450$, we can add a trailing zero to $3.45$ to get $3.450$. Since all digits are identical, $3.45 = 3.450$.
Explanation When comparing decimals, always begin with the largest place value on the left and move to the right. Align the decimal points to ensure you are comparing corresponding place values (ones to ones, tenths to tenths, etc.). The first pair of digits that are not equal will tell you which decimal is larger. If needed, you can add zeros to the end of a decimal without changing its value to make comparisons easier.
Common Questions
How do you compare two decimals to the thousandths place?
Align the decimal points and compare digits from left to right, starting at the largest place value. The first column where the digits differ determines which decimal is greater. Add trailing zeros to make both decimals the same length if needed.
What is an example of comparing decimals to the thousandths?
Compare 0.528 and 0.541: tenths are both 5 (same), hundredths are 2 vs 4 — since 2 < 4, we have 0.528 < 0.541. Compare 0.7 and 0.689: tenths are 7 vs 6 — since 7 > 6, we have 0.7 > 0.689 immediately.
What chapter covers comparing decimals in Illustrative Mathematics Grade 5?
Comparing decimals to the thousandths is covered in Chapter 5 of Illustrative Mathematics Grade 5, titled Place Value Patterns and Decimal Operations.
What inequality symbols are used to compare decimals?
Use > (greater than), < (less than), or = (equal to). For example, 0.528 < 0.541 (less than) and 0.7 > 0.689 (greater than). Equal decimals like 3.45 and 3.450 use the = symbol.
How do trailing zeros help when comparing decimals?
Trailing zeros extend a decimal to the same number of places as another without changing its value. For example, 3.45 = 3.450. With equal lengths, you can compare place value by place value without confusion.