Visualize decimals on a number line and compare them by place value from left to right.
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How to subdivide a number line to plot decimals.
To find a decimal like on a number line, we first look at the whole number part. Since it is and some extra, it lies between and .
We divide the space between and into equal parts (tenths). Taking the fourth mark after gives us the exact location of .
Rules for comparing two decimal numbers.
To find out which decimal is larger, we always start by comparing the most significant digits—the digits with the highest place value, reading from left to right.
If the whole number parts are equal, we compare the next smaller place value (tenths, then hundredths, and so on).
Visual of a number line being magnified at each decimal level.
Zooming in step-by-step reveals how precise decimal numbers are mapped between integers.
Example comparing 6.456 and 6.465.
Problem. Which is larger: or ?
To find out, we compare the corresponding digits at each place value, starting from the left (most significant digit).
Faded practice for identifying the closest number.
Let us compare the decimal numbers , , , and to identify which is closest to . First, we can arrange these numbers in ascending order around . This gives us . Next, we calculate the distance of each neighbouring number from . The distance from to is only hundredth away. Meanwhile, the distance from to is hundredths away. Since hundredth is a smaller distance than hundredths, the closest decimal to is .
MCQ identifying correct statements about decimal sizes.
Which of the following decimal numbers is the largest?
Free response problem to arrange a list of decimals.
Practice comparing decimals by writing the sequence from largest to smallest. Pay careful attention to the tenths and hundredths places.
List the five numbers separated by commas.
Explain how you decided which number was larger using place value.