In this Grade 7 Saxon Math Course 2 lesson, students learn to locate and name decimal numbers on a number line by dividing the intervals between whole numbers into 10 or 100 equal units, connecting place value concepts like tenths and hundredths to physical measurement. The lesson uses centimeter rulers and metersticks to practice expressing the same length in millimeters, centimeters, and meters using one- and two-place decimals. Students also practice arranging decimal numbers in order from least to greatest by identifying their positions on a number line.
Section 1
📘 Decimal Numbers on the Number Line
If the distance between consecutive whole numbers on a number line is divided by tick marks into 10 equal units, then numbers corresponding to these marks can be named using decimal numbers with one decimal place.
This is just the start. Next, you'll apply this concept through worked examples on reading scales, locating points, and ordering decimal numbers.
Section 2
Decimal Numbers on the Number Line
If the distance between consecutive whole numbers on a number line is divided into 10 equal units, marks can be named using decimals with one decimal place. If divided into 100 units, they can be named using two decimal places.
A line segment is past the 4 cm mark by 6 tiny ticks, so its length is cm.
On a number line from 8 to 9, an arrow pointing seven small marks after 8.3 is at .
The point marked X is two ticks past 0.7 on a line marked in hundredths, so the number is .
Imagine a ruler! The big numbers are whole units, and the tiny ticks in between are the decimal parts. Splitting a space into 10 pieces creates tenths (like 0.1, 0.2), which is perfect for measuring things that don't land exactly on a whole number.
Section 3
Converting Metric Units With Decimals
Since 1 meter equals 100 centimeters, each centimeter is of a meter, which can be written as m. An object 25 cm long is also 0.25 m long.
A bookshelf is 75 cm tall. Since 1 cm is m, the bookshelf is meters tall.
A student's desk is 1.45 meters wide. To convert to centimeters, we multiply by 100, so it is cm wide.
A one-foot ruler is about 305 mm long, which is the same as 30.5 cm or 0.305 m.
Changing metric units is like magic—just move the decimal! Since 100 centimeters make up one meter, any length in centimeters is just a 'part' of a whole meter. We write these hundredth parts using decimals, which makes converting between units a snap.
Section 4
Ordering Decimal Numbers
To order decimal numbers, compare their whole number parts first. If they are equal, compare the digits in the tenths place, then the hundredths place, and so on, moving from left to right.
To order , we look at the tenths place to arrange them from least to greatest: .
To compare and , we can write as . Since is greater than , we know .
The numbers cm and mm are equal because 1 cm equals 10 mm, so .
Think of it like a high-score game! First, check the whole numbers. If they're tied, look at the tenths place—the bigger digit wins. Still tied? Move to the hundredths place. Just add zeros to help compare, like turning 4.5 into 4.50!
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Section 1
📘 Decimal Numbers on the Number Line
If the distance between consecutive whole numbers on a number line is divided by tick marks into 10 equal units, then numbers corresponding to these marks can be named using decimal numbers with one decimal place.
This is just the start. Next, you'll apply this concept through worked examples on reading scales, locating points, and ordering decimal numbers.
Section 2
Decimal Numbers on the Number Line
If the distance between consecutive whole numbers on a number line is divided into 10 equal units, marks can be named using decimals with one decimal place. If divided into 100 units, they can be named using two decimal places.
A line segment is past the 4 cm mark by 6 tiny ticks, so its length is cm.
On a number line from 8 to 9, an arrow pointing seven small marks after 8.3 is at .
The point marked X is two ticks past 0.7 on a line marked in hundredths, so the number is .
Imagine a ruler! The big numbers are whole units, and the tiny ticks in between are the decimal parts. Splitting a space into 10 pieces creates tenths (like 0.1, 0.2), which is perfect for measuring things that don't land exactly on a whole number.
Section 3
Converting Metric Units With Decimals
Since 1 meter equals 100 centimeters, each centimeter is of a meter, which can be written as m. An object 25 cm long is also 0.25 m long.
A bookshelf is 75 cm tall. Since 1 cm is m, the bookshelf is meters tall.
A student's desk is 1.45 meters wide. To convert to centimeters, we multiply by 100, so it is cm wide.
A one-foot ruler is about 305 mm long, which is the same as 30.5 cm or 0.305 m.
Changing metric units is like magic—just move the decimal! Since 100 centimeters make up one meter, any length in centimeters is just a 'part' of a whole meter. We write these hundredth parts using decimals, which makes converting between units a snap.
Section 4
Ordering Decimal Numbers
To order decimal numbers, compare their whole number parts first. If they are equal, compare the digits in the tenths place, then the hundredths place, and so on, moving from left to right.
To order , we look at the tenths place to arrange them from least to greatest: .
To compare and , we can write as . Since is greater than , we know .
The numbers cm and mm are equal because 1 cm equals 10 mm, so .
Think of it like a high-score game! First, check the whole numbers. If they're tied, look at the tenths place—the bigger digit wins. Still tied? Move to the hundredths place. Just add zeros to help compare, like turning 4.5 into 4.50!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter