Chapter 5
Decimals
A price tag reads 3.49. A stopwatch reads 9.58 seconds. A tape measure lands between two marks, and the number written down is 2.5. None of those amounts is whole, yet none of them needs a new kind of symbol either: the same ten digits do the work, and the only extra mark is a single dot. Numbers written that way are called decimals, and that one dot is what lets our counting system carry on below one. How much can a single mark really change?
What You'll Explore
4 lessons.
- Decimal Place Value
Which is larger, 0.7 or 0.65? Counting digits gives one answer and the number line gives another. This lesson follows the place value columns past the decimal point to find what each new column is worth, and what that says about zeros sitting at the end of a decimal.
- Operations with Decimals
Adding 3.4 and 2.7 looks a lot like adding 34 and 27, until you have to say where the point goes in the answer. Multiplying and dividing raise the same question in their own ways. This lesson takes the four operations one at a time and works out what the point does to each.
- Converting Between Fractions and Decimals
One half becomes 0.5 without any fuss, but one third starts a string of threes that never ends. Both forms are supposed to name the same amount. Here you will see how a fraction and a decimal turn into each other, and what decides whether the digits stop or keep repeating.
- Rounding and Estimation
A calculator can hand back 8.472916 when all anybody needed was a rough answer. Cutting a number short has to follow some rule, or two people would shorten it differently. This lesson looks at what makes one shortened answer the right one, and at when a quick approximate figure is worth more than an exact one.