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Locating And Comparing Decimals

Visualize decimals on a number line and compare them by place value from left to right.

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Locating Decimals on a Number Line

How to subdivide a number line to plot decimals.

Locating Decimals on a Number Line

To find a decimal like $1.4$ on a number line, we first look at the whole number part. Since it is $1$ and some extra, it lies between $1$ and $2$ .

We divide the space between $1$ and $2$ into $10$ equal parts (tenths). Taking the fourth mark after $1$ gives us the exact location of $1.4$ .

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Comparing by Place Value

Rules for comparing two decimal numbers.

How to Compare Decimals

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).

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Number Line Magnification

Visual of a number line being magnified at each decimal level.

$Locating and Comparing Decimals$

Click to zoom

Zooming in step-by-step reveals how precise decimal numbers are mapped between integers.

Which is larger?

Example comparing 6.456 and 6.465.

Problem Statement

Problem. Which is larger: $6.456$ or $6.465$ ?

To find out, we compare the corresponding digits at each place value, starting from the left (most significant digit).

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Finding the Closest Decimal

Faded practice for identifying the closest number.

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Let us compare the decimal numbers $0.9$ , $1.1$ , $1.01$ , and $1.11$ to identify which is closest to $1$ . First, we can arrange these numbers in ascending order around $1$ . This gives us $0.9 < 1 <$ $< 1.1 < 1.11$ . Next, we calculate the distance of each neighbouring number from $1$ . The distance from $1$ to $1.01$ is only hundredth away. Meanwhile, the distance from $1$ to $0.9$ is $10$ hundredths away. Since $1$ hundredth is a smaller distance than $10$ hundredths, the closest decimal to $1$ is .

Smallest and Largest

MCQ identifying correct statements about decimal sizes.

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Which of the following decimal numbers is the largest?

Arranging in Descending Order

Free response problem to arrange a list of decimals.

Arrange the following quantities in descending order: 33.13 m, 33.31 m, 33.133 m, 33.331 m, 33.313 m. Explain your reasoning.

Practice comparing decimals by writing the sequence from largest to smallest. Pay careful attention to the tenths and hundredths places.

Descending Order (Largest to Smallest)*

List the five numbers separated by commas.

Explanation of Place Value*

Explain how you decided which number was larger using place value.

← previousUnits Of Measurement next →Addition And Subtraction Of Decimals

Locating Decimals on a Number Line

How to subdivide a number line to plot decimals.

Locating Decimals on a Number Line

To find a decimal like $1.4$ on a number line, we first look at the whole number part. Since it is $1$ and some extra, it lies between $1$ and $2$ .

We divide the space between $1$ and $2$ into $10$ equal parts (tenths). Taking the fourth mark after $1$ gives us the exact location of $1.4$ .

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Which is larger?

Example comparing 6.456 and 6.465.

Problem Statement

Problem. Which is larger: $6.456$ or $6.465$ ?

To find out, we compare the corresponding digits at each place value, starting from the left (most significant digit).

1 / 4

Finding the Closest Decimal

Faded practice for identifying the closest number.

0 of 3 blanks filled

Smallest and Largest

MCQ identifying correct statements about decimal sizes.

1 / 5

Which of the following decimal numbers is the largest?