Lessons 33: Comparing Decimals, Rounding Decimals

New Concept

To compare or round decimals, we use place value. Aligning decimal points helps compare digits, and terminal zeros can be added or removed without changing value.

What’s next

This is the foundation for all decimal operations. Soon, we’ll tackle worked examples on ordering, comparing, and rounding various decimal numbers to solidify your understanding.

Property

When comparing decimal numbers, it is necessary to consider place value. Aligning decimal points can help to compare decimal numbers digit by digit. It may be helpful to insert terminal zeros so that both numbers will have the same number of digits to the right of the decimal point, since terminal zeros do not add value.

Examples

• Compare $0.12$ and $0.012$. We add a zero to the first number to get $0.120$. Since $120$ thousandths is greater than $12$ thousandths, we know $0.12 > 0.012$.
• Compare $0.4$ and $0.400$. Since terminal zeros don't change the value, we can see that $0.4 = 0.400$.
• Compare $1.1$ and $1.099$. We can add two zeros to the first number to get $1.100$. Since $1.100$ is greater than $1.099$, we have $1.1 > 1.099$.

Explanation

Think of it like a Wild West duel! To see which decimal is bigger, line up their decimal points. If needed, add zeros to the end of one number so they both have the same number of digits. Now, compare them from left to right, place by place, to declare the undisputed champion of value!

Property

To round decimal numbers, we can use the same procedure that we use to round whole numbers. After rounding decimal numbers, we should remove terminal zeros to the right of the decimal point because they are not needed as placeholders.

Examples

• Round $3.14159$ to the nearest hundredth. We underline the 4 and circle the 1: $3.1\underline{4}①59$. Since $1 < 5$, the 4 stays, giving us $3.14$.
• Round $38.62$ to the nearest whole number. We underline the 8 and circle the 6: $3\underline{8}.⑥2$. Since $6 \ge 5$, the 8 rounds up to 9, giving us $39$.
• Round $4396.4315$ to the nearest hundred. We underline the 3 and circle the 9: $4\underline{3}⑨6.4315$. Since $9 \ge 5$, the 3 rounds to 4, resulting in $4400$.

Explanation

Rounding is like giving a number a 'close enough' makeover. Find your rounding spot, then peek at the digit next door. If it's 5 or bigger, your target digit gets a promotion and rounds up! If not, it stays put. Afterwards, clean up by tossing any trailing zeros after the decimal point for a tidy finish.