Lesson Guide
Explanation
Between 3 and 4 there are lots of numbers. You already know one way to write them, using fractions: three and a half is 3 and 1/2. Decimals are a second way of writing exactly the same thing, and the reason they are worth learning is that they fit straight into the place-value columns you already know. No new system — just the chart carrying on past the ones column.
Your Turn
Name something measured with a number between two whole numbers. Check: your height, a running time, a price — all of them.
Watch Out
A decimal is not a different kind of number. 3.5 and 3 and 1/2 are the same amount written two ways.
Explanation
Here is the place-value chart you know, with two new columns bolted on the right. Going left, each column is ten times bigger — ones, tens, hundreds. Going right it keeps working, just the other way: each column is ten times smaller. So after the ones comes tenths, then hundredths. The dot, called the decimal point, simply marks where the whole numbers stop and the parts begin.
Your Turn
Which is bigger, one tenth or one hundredth? Check: one tenth — the further right you go, the smaller the pieces.
Watch Out
The decimal point is a marker, not a column. Nothing lives in it.
Explanation
Take 2.47. The 2 is two whole ones. The 4 sits in the tenths column, so it is four tenths. The 7 sits in hundredths, so it is seven hundredths. Look at the two bars: four tenths is a big chunk, seven hundredths is a thin sliver, even though 7 is the bigger digit. And when you say it aloud, read the digits one at a time after the point — two point four seven, not two point forty-seven.
Your Turn
In 5.83, what is the 8 worth and what is the 3 worth? Check: 8 tenths and 3 hundredths.
Watch Out
Saying 'two point forty-seven' makes 0.47 sound like 47. Read the digits singly.
Explanation
This is the one to be careful with. 0.5 means five tenths, which is half. 0.05 means five hundredths, which is a tiny sliver — ten times smaller. The only difference is a zero, and that zero is doing real work: it holds the tenths column empty so the 5 stays in hundredths. Leave it out and the 5 slides one column left, making the number ten times bigger. This is exactly the job zero does in 405 versus 45.
Your Turn
Which is bigger, 0.3 or 0.03? And how many times bigger? Check: 0.3, and it is ten times bigger.
Watch Out
A zero straight after the decimal point changes everything. 0.07 is not the same as 0.7.
Explanation
Decimals are already all around you. A price like four dollars seventy-five is written 4.75, because there are 100 cents in a dollar, which makes each cent one hundredth. That is exactly why prices always show two decimal places. Heights, race times and temperatures all use them too. Money is the most useful one to hold on to, because you already know how it behaves — and it is a decimal with hundredths, which is precisely what this chapter is about.
Your Turn
Write three dollars and twenty cents as a decimal. Check: 3.20, or 3.2 — the same amount.
Watch Out
$4.7 looks like 4 dollars 7 cents but means 4 dollars 70 cents. With money, always write both places.
📌 Key Points — this lesson in a nutshell
- The place-value chart carries on past the ones: tenths, then hundredths.
- Each step right is ten times smaller.
- The decimal point marks where whole numbers stop — it is not a column.
- Read digits singly after the point: "two point four seven".
- 0.5 is ten times bigger than 0.05. The zero holds the tenths column empty.
- Money is a decimal you already know: 100 cents in a dollar means cents are hundredths.
Step 1: Introduction
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