Lesson 40: Using Zero as a Placeholder

New Concept

When calculating with decimals, we fill empty places with a zero. This holds the place value and keeps numbers aligned for correct subtraction or multiplication.

In order to subtract, it is sometimes necessary to attach zeros to the top number.

What’s next

This is a foundational skill for decimal operations. Soon, you'll work through examples using placeholder zeros in subtraction, multiplication, and writing decimal numbers.

Property

When subtracting, multiplying, and dividing decimal numbers, we often encounter empty decimal places. When this occurs, we will fill each empty decimal place with a zero.

Examples

• $0.6 - 0.42 \rightarrow 0.60 - 0.42 = 0.18$
• $5 - 0.8 \rightarrow 5.0 - 0.8 = 4.2$
• $0.4 \times 0.2 \rightarrow \text{multiply } 4 \times 2 = 8, \text{ then place decimal to get } 0.08$

Explanation

Think of zero as a trusty sidekick for your decimals! When you're subtracting or multiplying, sometimes there's an empty spot. Just pop a zero in there to hold the place. This little hero ensures all your numbers line up perfectly for subtraction and that your decimal point lands in the right spot after multiplying. It's an easy trick!

Property

Circle graphs, which are sometimes called pie graphs or pie charts, display quantitative information in fractions of a circle.

Examples

• Total items: For a graph showing 10 cars, 5 trucks, and 5 bikes, the total is $10 + 5 + 5 = 20$ vehicles.
• Finding the fraction: If 5 out of 20 vehicles are trucks, the fraction is $\frac{5}{20}$, which simplifies to $\frac{1}{4}$.
• Finding the percent: Since $\frac{1}{4}$ of the vehicles are trucks, that portion of the graph represents $25\%$ of the total.

Explanation

Imagine your data is a giant pizza! A circle graph, or pie chart, slices it up to show how much of the whole each part represents. Instead of just reading boring numbers, you can see at a glance which slice is the biggest. It's a super visual tool for comparing parts of a group to the entire thing.

Property

The number of decimal places in a product is the sum of the decimal places in the factors.

Examples

• $0.5 \times 0.3 \rightarrow 5 \times 3 = 15$. Two total decimal places gives $0.15$.
• $0.12 \times 0.5 \rightarrow 12 \times 5 = 60$. Three total decimal places gives $0.060$ or $0.06$.
• $(0.4)^2 = 0.4 \times 0.4 \rightarrow 4 \times 4 = 16$. Two total decimal places gives $0.16$.

Explanation

Multiplying decimals is a two-step dance! First, ignore the decimal points and multiply the numbers like they're whole. Next, count the total number of decimal places in the original numbers you multiplied. Your final answer must have that same number of decimal places. Just count from the right and place your point. Easy peasy!