Exercises: comparing decimal numbers

Compare 3.60 and 3.61.

Compare 0.5 and 0.23.

Compare 2.7 and 2.70.

Compare 0.08 and 0.1.

You can start from 3 and add a 0.1 for each tick you jump to the right.

Or you start from 4 and subtract a 0.1 for each tick you jump to the left.

$x=3.4\backslash textcolor\{0080FF\}\{x\}=3.4$

$y=3.9\backslash textcolor\{60B000\}\{y\}=3.9$

On the number line, the piece between $0.10.1$ and $0.20.2$ is divided into $1010$ sections.

Calculate the distance between $0.10.1$ and $0.20.2$ (as in part a)).

$0.2-0.1=0.10.2-0.1=0.1$

Divide the number $0.10.1$ into 10 parts.

$0.1:10=\frac{1}{100}=0.010.1:10\; =\; \backslash frac\{1\}\{100\}\; =\; 0.01$

Each section therefore corresponds to $0.010.01$.

First number:

Count off at which section the left-hand decimal number is located.

The left-hand number is behind the second section:

$0.1+2\cdot 0.01=0.120.1+2\backslash cdot0.01=0.12$

In other words, you had to add 2 hundredths to the number $0.10.1$.

Second number:

Count off at which section the right-hand decimal number is located.

The right-hand number is behind the seventh section.

$0.1+7\cdot 0.01=0.170.1+7\backslash cdot0.01=0.17$

In other words, you had to add 7 hundredths to the number $0.10.1$.

You can see from the number line or by comparing the decimal numbers that the second number is greater than the first one. So,